Greenland is four times the size of France, but with a population of only 57,000 - and as its huge ice sheets begin to melt, it could find itself sitting on a fortune in oil and gems. Now, it has voted to cut all ties with its Danish rulers. Patrick Barkham reports from a nation in the making

From the air, the largest island on the planet not to be its own continent, or even a nation, is so white and featureless that it resembles a soft cloud. On the ground, hard snow is driven into black rock, and the cold slaps you in the face. When people stomp indoors, icy air clings to them like a shroud.

In the past, the chill has killed off entire civilisations in Greenland. Even today, wrapped in fat rolls of designer polar wear or cosseted in climate-controlled SUVs, life is tough. Late last month, however, the 57,000 people who inhabit this harsh land took a firm step further into the cold when a decisive majority voted "aap" - yes - to seeking complete independence from Denmark, their colonial master for nearly 300 years.

Reverberations from Greenland's desire to go it alone will be felt far beyond this icy coastline. What happens here could have a bearing on the fate of the globe. As new seaways open, and melting ice exposes new farmland and valuable minerals, this emerging nation will be shaped, in the literal sense, by climate change. Its newly independent citizens will find themselves the custodians of a pristine Arctic land beneath which may lie oil and diamonds and rubies of stupendous value - not just to Greenland but to the rest of the world.

When it does shake off the last of its colonial shackles, Greenland will become the newest and the most extraordinary country in the world, as well as one of the most isolated. Although its remote north-west coast is little more than 100 miles from Canada's Ellesmere Island, it is nearly 2,000 miles from Europe. Four times the size of France, Greenland contains the longest fjord and largest national park in the world; 85% of its territory is covered with ice. Ten per cent of the world's fresh water is frozen on Greenland's ice-sheet; if it melts, sea levels will rise by seven metres, sweeping away capital cities and countries around the world.

There are no roads to anywhere in Greenland but in the capital, Nuuk (population 14,719), all streets seem to lead to Aleqa Hammond. From old people buying hunks of porpoise at the market to teenage sports fans at the indoor handball game, everyone mentions the former finance and foreign minister. Like every Greenlander, her family is in the (slim) phone book so I call up and am invited round.

Some predict that Hammond, 43, will be the first prime minister of an independent Greenland. She lives in a fairytale wooden house overlooking the gloomy waters of Nuuk's old harbour. Inside her door, a wolf skin hangs from its head. On her living room shelves are delicate Greenlandic artworks set between two walrus jaws and a pair of polar bear skulls. Above her sofa is a pale spike that looks as if it was plucked from a unicorn's head: it is the tusk of a narwhal.

"My mother just called to say my brother is coming to town with a narwhal. So it's a happy time - whale is Christmas food in Greenland," she beams. Almost nine out of 10 Greenlanders are Inuit or Inuit/Danish. Hammond eloquently embodies the traditional and the modern: her husband is Danish, but the other members of her family are traditional hunters from Uummannaq, in the remote north, where thousands still live from hunting seals, whales and polar bears. Hammond's father died when she was seven. He fell through the ice on a hunt with his dog team. "I feel pride in being a Greenlander," she says. "I see possibilities in everything. This is a gift I think I can give to others - making impossible things possible."

Hammond went to university in Montreal and is fluent in Greenlandic, Danish, English and German - a legacy of six years backpacking. She became a member of Greenland's 31-person parliament (nearly half the MPs are women) in 2005 and was instantly elevated to a ministerial position in Greenland's "home rule" government, a local administration with power devolved from Copenhagen. "When I was 13, in 1979, we got home rule in Greenland. It was a gift given to me in my teenage years. The referendum is a new gift for the next generation and that is self-governance," she says. The referendum result now allows Greenland to gradually "take home" responsibility for policing, the judiciary and other aspects of society still under Danish control. When Greenland no longer needs Denmark's financial help, it will finally become a fully independent nation. Many Greenlanders think this could still be more than a decade away. "I believe that Greenland will achieve independence during the time I am still active in politics," says Hammond.

If Hammond represents the future, Greenland's past is vividly retold by Thorkild Kjærgaard, head of history and culture at the University of Greenland, a sleek new Scandinavian block set on a rough hill above Nuuk, close to a rocky golf course. (Football is Greenland's national sport but it can't join Fifa because it hasn't got a single grass pitch.)

Geographically, Greenland belongs to the North American continent. Nuuk is closer to New York than Copenhagen. Historically, it has been tied to Europe. Culturally, and linguistically, it is now unique. "When Christopher Columbus arrived in North America in 1492 there were hundreds of native languages there. Today all American heads of states address their people in Portuguese, Spanish, English and French. The only 'head of state' who does not address his people in a European language is here," says Kjærgaard, a tall, intense Dane, who has worked in Greenland since 2002. "Greenlandic is the only American language that has been preserved."

The reason, he argues, is the Danes. For hundreds of years, they treated Greenland and its people with unprecedented respect; Greenlandic and Danish are both official languages. According to Kjærgaard, there is no record of a Dane killing an Inuit in the 18th and 19th centuries; thousands were slaughtered in the US. Hammond agrees. "Thank God it was the Danes who colonised us, not the British or Americans or Dutch or Germans," she says. "The Danes respected our lifestyle and culture and that has made it possible for us to maintain our own identity as a people."

The reason for this exceptional colonial history, thinks Kjærgaard, is not that the Danes were uniquely civilised (they were more typical colonial oppressors in the Caribbean) but because the Norwegian-Danish kingdom had a grand passion for Greenland. Nordic people travelled hundreds of miles beyond Iceland to first settle here in the 10th century. Some suggest that lonely Erik the Red jokingly named it "green" to fool his fellow Vikings into joining him, although southern Greenland was actually a lush colour compared with Iceland. The Norwegians disappeared from Greenland during the 15th century but the Danish-Norwegian kingdom returned in 1721 to "recover" the old country. After the Danish-Norwegian kingdom broke up, Denmark inherited Greenland with a keen sense of duty.

"Greenlanders were treated like Danish citizens and their language was part of the pride of the kingdom. It showed the immensity of the Danish empire," says Kjærgaard. Danish missionaries also believed native people could only take the word of God to their hearts if it was in their own language. They helped turn Greenlandic into a written language in the mid 19th century. Greenland even launched a native-language newspaper in 1861, curiously one of the first in the world to have colour illustrations. (Absent in the landscape, primary colours are big in Greenland; Nuuk's houses are painted bright yellow, red, blue and green.)

Today, Kjærgaard feels that Greenland's rejection of its enlightened old master is equally emotional. Compared with indigenous Arctic people in Canada, the United States and Russia, Greenlanders are financially well supported and have their own government. "Seen from a pan-American perspective, Greenland is a fantastic success," says Kjærgaard. Independence "is driven by passion, the idea of a self-sustaining Inuit nation. They are not satisfied with being what they are today - the king nation of the north, subsidised by Copenhagen." He believes Greenland is better off under the warm financial wing of Denmark, which gives Greenland 3.2bn kroner (£365m) every year.

Some Greenlanders, however, experience the Danish influence less benevolently. At this time of year in Nuuk, the sun seems perpetually beyond the horizon. Where its weak fingers touch the land, it turns white peaks raspberry. Families hunker down indoors, hanging illuminated orange paper stars in their darkened windows. Further north, in Disko Bay, where linguist Nuka Moller grew up, families hunt in the perpetual night by sound, listening for the narwhals' blowing before they strike with the harpoon. Rather than hunt whales, Moller is creating a Greenlandic grammar check for computers. He finds a lingering Danish elite can still patronise indigenous people. "A segment of society still has that mind-set: 'Are you really able to take care of yourself?' I felt like I was going back 30 years during recent debates over independence," he says. In those days, the colonial sense of superiority was explicit: he remembers his radio telegrapher father teaching Morse code to Danes, who would quickly become his boss.

"We are hopefully growing out of our teenage years in Greenland and going into adulthood," says Moller - an analogy echoed by many people picking their way carefully across the ice in Nuuk. Torben Heckmann, a Danish police officer seconded to help Greenlandic investigations, finds local people very kind, but when it comes to independence, he pauses. "They are a little bit like spoilt children. They want it all but they don't want to pay for it," he says. "They are short of teachers, IT workers, bankers, doctors, police and dentists - they have to realise they can't do it all themselves."

Some young Greenlanders feel oppressed by the ongoing Danish influence. Lena Broberg, 21, is studying Greenlandic at the university. Only one of her lecturers is a Greenlander; all lessons are in Danish. "We can't really use our language in our own country. If we want to have an education it has to be in Danish. It's very sad," she says. "The way Danes and Greenlanders think is so different. We can't really understand each other. Our sense of humour is totally different. Danish people are more serious and they talk too much. They organise what they are going to do at 3pm the next day. We don't do that."

If a passion for identity is driving independence, colder financial calculations also play a part: there is money beneath the ice, and why should the Greenlanders share it with Denmark? But the treasure hasn't been found yet, and in the meantime the country is very much dependent on Denmark. Before westerners arrived, the Inuit were self-sufficient, but now self-sufficiency for such a tiny population seems impossible. Greenland is not rich, and shrimping - vulnerable to climate change - remains its biggest industry and export (although several companies are looking at the unlimited potential of marketing melted ice water). Most food is imported from Denmark; 97% of its trade is with the EU.

In September Hammond resigned from the government in protest over the size of Greenland's budget deficit. She now makes light of the funding gap if the country lost its Danish subsidy. "Taking the future in your own hands has a fantastic psychological impact," she says. "It will free us from our dependency on Denmark. An independent Greenland is much closer than we think."

Denmark and Greenland agree that independence will only be granted when the Danish subsidy is no longer needed. Some fear this may drive Greenland into the arms of more dangerous allies. "If you close the door to Denmark, you open the door to big American business," says Kjaergaard. "If Greenland becomes completely independent they will become dependent on American capital and on very heavy and environmentally dangerous exploitation of natural resources. The price of independence will be very high."

Many in Greenland believe exploiting it's a price worth paying, however, and prospectors are scouring the country for zinc, lead and precious stones including diamonds and rubies, which have been found in southern Greenland. Hammond speaks enthusiastically about the prospects for a second gold mine, due to open next year, and claims five "huge" new mines will open in the next seven years. "Other countries have a tendency to see the Arctic as an area with no people," she says. Independence ensures that Greenlanders will get full rights to their "underground" and their waters, as lucrative new shipping routes - such as the Northwest Passage - open up. Oil is another tantalising prospect. "We know there is oil in Greenland. You can see it, you can touch it in the Disko Bay area," she says.

Making the best of global warming - everyone comments on the unseasonable slush in Nuuk - is also trumpeted in a more cautious, less effervescent style, by Hammond's big rival, Hans Enoksen, Greenland's current home rule prime minister. Like Hammond, he comes from a remote village and defends Greenlanders' ancient right to hunt "mammals of the sea"; unlike her, he insists on speaking Greenlandic, and has won great support for this, proving you don't need Danish to lead Greenland. (Intriguingly, some critics claim Enoksen's apparent lack of linguistic skills is tactical; they allege he could speak Danish perfectly well when younger.)

"In terms of fishing and farming, global warming has meant there are better conditions for the livestock. There are increased cod fisheries which will also have a significant effect on our economy. And because of receding glaciers there are more possibilities for mineral exploration," he says, sitting in shirtsleeves in his modest office in central Nuuk. "But we have no interest in extracting for extraction's sake. We have to be responsible and stress sustainable development."

Hammond, too, says monitoring the environmental impact of Greenland's economic development must be the nation's priority and it will set tough standards for mining and oil companies. "Greenlanders' heart is the environment. You can't sell your heart for oil," she says.

Enoksen claims that Greenlanders "have not been the cause of the extinction of a single mammal in our environment". But a biologist (who asked not to be named) who works with Greenland's government to set sustainable quotas for its hunting doubts its commitment to protecting its land from hunters or miners. Narwhals and beluga whales are declining but, faced by angry hunters, Greenland's politicians recently raised the annual quota for beluga whales by 100 animals. Recommended quotas are routinely breached, even without all the illegal hunting. Greenland's seven hunting officers can't hope to police this vast land. While hunters complain the lack of sea ice has stopped winter hunting with dogs, global warming has enabled them to kill polar bears from boats instead.

"Greenland should set much higher standards for environmental protection on mining and oil exploration," the biologist says. "Each time there is a new gold mine everybody is really thrilled and thinks, 'This is the solution to all our problems.'"

If Greenland's financial independence is sealed by a big oil or mineral find, the geopolitical implications are fascinating. The United States still maintains an air base in northern Greenland, but would American companies win the race to exploit its resources? Would Russia stand idly by? How robustly independent could a nation of 57,000 people be? Alcoholism and suicide are already social problems; how would oil-rich Greenlanders cope with being outnumbered by foreign workers in its new mines and oilfields? And what will happen to all that melting ice?

Hammond says she will challenge Enoksen for the leadership of his party - and the government - next year. Both politicians, however, insist a fully independent Greenland will be strong enough to prevent the exploitation of its people and ruination of its landscape. "We have a very strong parliament and a politically aware population," says Hammond. Even if its tiny cohort of parliamentarians are offered inducements beyond their wildest dreams? "We don't have bribes in Greenland. Our democracy is strong enough," she insists.

In the aftermath of the referendum, Nuuk's radios were tuned to a parliamentary debate on self-governance. Amidst the Greenlandic, one English phrase kept popping out: "Yes we can." For Kjærgaard, it was a sign of Greenland's likely future direction. "They accept the language of colonisers and believe that here is a man to admire," he says. "Barack Obama is a fine person. It is said it is unbelievable that Obama could become president of the US but only when a native American moves into the White House could you truly say everything is possible in the US."

Perhaps, however, a people who have stubbornly carved livelihoods from snow and rock and sea for centuries can resist baleful outside influences. After several repetitions of "yes we can" during the debate, one Greenlandic politician interrupted to point out that it could actually be said in Greenlandic. "Qaa sapinngilagut!" he shouted. Translated back into English, it became as unique as the people who were taking it to heart: "Yes, come on, you."