Hundreds of thousands of Syrian refugees are enduring blizzards, biting winds and freezing rain as the worst winter storm for decades sweeps across the Middle East.

Aid agencies are warning of extreme hardship, particularly among families living in flimsy tents.

The United Nations has said it is extremely concerned about the plight of refugees. Aid agencies are trying to distribute thermal blankets, heaters, clothing and tarpaulin sheeting but are facing logistical difficulties in some areas due to severe weather conditions.

"For the hundreds of thousands of refugees in Lebanon, as well as those in neighbouring countries and the displaced in Syria, a storm like this creates immense additional hardship and suffering," said Amin Awad of the UN refugee agency, UNHCR, in Lebanon.

The storm, named Alexa, has brought snow, hail, driving rain and icy winds to the region, with the Bekaa Valley in Lebanon particularly badly hit. Parts of the region are forecast to see up to 10cm of snow in the coming days.

According to Oxfam, around two-thirds of the 1 million Syrian refugees in the country have settled in the Bekaa Valley and north Lebanon, which are especially prone to harsh winter conditions.

Many refugees in Lebanon are living in unofficial makeshift camps, with shelters built from scavenged materials. The Lebanese government has refused to establish refugee camps for fear that they will become permanent homes for Syrians who have fled the civil war.

Images from the area showed refugees scraping snow off the roofs of tents, icicles hanging from ropes and wooden posts, and laundry frozen on washing lines.

Temperatures have also plummeted in Jordan and Turkey this week. Many refugees have only the thin summer clothes in which they fled Syria, and are now sleeping on thin mats or blankets laid on the freezing ground.

"The severe snowstorm this week in Lebanon and Jordan is just the beginning of winter misery for the hundreds of thousands of Syrian refugees struggling to combat the bitterly cold and wet conditions," said Nigel Timmins of Oxfam.

"Many families are facing winter in makeshift tents and unfinished buildings, unable to afford to buy fuel to run heating stoves, extra clothing or blankets. Flimsy tents are prone to flooding and are likely to collapse under the weight of snow."

The charity is warning that overcrowding exacerbated by cold conditions could help spread respiratory illnesses among refugee families.

According to Ahmed Baroudi, a field worker for Save The Children who has spent the past few days among refugees in the Bakaa Valley, many of the families' makeshift shelters are leaking badly. "The winds have torn the plastic sheeting, and the ground has become like a swamp," he told the Guardian.

"Many of the children don't have proper shoes, they are wearing flip flops, and most only have summer clothing. Some families have small stoves but can't afford wood, so they are burning plastic bags and grocery boxes. It's very dangerous for the children to breathe the smoke from these fires. But they told me: 'We have two choices – freeze to death, or die from the smoke'."

A refugee named only as Ibrahim, 27, told Reuters: "The storm will finish us. It's freezing now. I seek refugee in God." His children were huddled round a fire in a metal crate in the corner of his tent as strong winds blew snow in the entrance. The dirt floor had turned to mud.

Marion McKeone, also of Save The Children in Lebanon, said that although the storm was harsh, weather conditions in the Bakaa Valley would be severe for the next four months. "We are expecting things to get worse as the winter progresses," she said.

The worst of the storm has bypassed Camp Za'atari in northern Jordan, although the area was hit by heavy rain and wind, toppling at least 10 tents on Thursday, leaving residents vulnerable to freezing temperatures.

"It was very cold, windy and muddy and all I was able to think of is how to protect my wife and four children," Ali Shatri, a 36-year-old refugee told Reuters. He said aid workers quickly evacuated him and other families whose tents were blown down to other secure areas in the camp.

Killian Kleinschmidt, the camp's manager, told the Guardian: "The electricity supply is a bit iffy because so many people are switching on electrical heaters. We know where the weak spots are, and we are doing drainage work and making contingency arrangements." Winter clothing, blankets and gas heaters were being distributed."

About 3,000 families out of the camp's total population of 82,000 were still living in tents, he added. About 700 new refugees were currently arriving each night, and some who had left Za'atari to live in Jordanian villages and towns were returning as conditions at the camp improved, he said.

The UN called off its first cross-border airlift of twelve plane-loads of humanitarian supplies from Iraq to north-east Syria because of the storm. Agencies are also reporting that the distribution of emergency cold weather supplies has been hampered by snow blocking roads in some areas.

According to UNHCR, there are 2.3 million Syrian refugees around the region, at least half of them children. Some are beginning their third winter in temporary homes, although the numbers fleeing Syria have sharply accelerated over the past year.

The severe winter deluge also affected Palestinians in the Gaza Strip, with more than 30 people injured in car crashes and as poorly built homes collapsed in the icy rain.

Meanwhile, Iran and Saudi Arabia have both been invited to attend the Geneva 2 peace conference on Syria next month, diplomats have said. The presence of countries which are respectively strong supporters of President Bashar al-Assad and the armed opposition to him seems certain to guarantee extremely tough talks.

According to sources quoted by the AFP news agency, 32 countries are to be invited to the January 22 conference, which is aimed at mapping out a political transition to end nearly three years of fighting in Syria that has killed more than 120,000 people.

The Syrian government and the opposition will each send delegations and will hold bilateral talks hosted by the UN-Arab League envoy Lakhdar Brahimi. The invitations are expected to be issued by the UN secretary-general Ban ki-Moon, by the end of the year. Russia, also backing Assad, has pushed hard for Iran to be invited.

A spokesman for Syria's main western-backed rebel group criticised a US-British decision on Wednesday to suspend non-lethal aid to opposition fighters in northern Syria.

The decision came after Islamic militants seized warehouses containing US military gear that was intended for the western-backed main rebel faction.

"We believe it was a hasty decision and we are in contact with our British and American friends … to reconsider this decision," rebel spokesman, Loay al-Mikdad, told Reuters.

He said the suspension of aid will have negative effects on the Syrian people and not only the Free Syrian Army (FSA). "The Syrian people need every assistance and we believe that the American and British friends will review this decision," he said.

US and British officials said on Wednesday that humanitarian aid such as food and blankets would not be affected by the suspension.

The warehouses taken over by opposition factions belonged to the FSA's supreme military council, led by General Salim Idris, a secular-minded, western-backed moderate.