In summer, the Grand Canyon is all crowds and traffic jams. In winter you can have one of the most awe-inspiring places in the world to yourself

'I have heard rumours of visitors who were disappointed," JB Priestley once said about the Grand Canyon. "The same people will be disappointed at the Day of Judgment."

I have to confess I was disappointed on my first visit to the canyon, more than a decade ago. One July, on our way to Los Angeles, my family and I swung off the highway, made the 60-mile detour to the South Rim, and found ourselves caught in a long traffic jam. When we eventually managed to park, and walked to the rim, the scale of the sight off the edge was so great it was hard to muster a response. It was so vast, and so familiar from pictures, it might just as well have been a picture. What impressed me most was the Babel of languages audible among the visitors pouring off the tour buses. It sounded like Times Square on a Saturday night, with every continent represented in the hubbub.

At this magnitude, scale is deceptive. Pedro de Castañeda, a Spaniard on the Coronado expedition of 1540, whose members were among the first Europeans ever to see the canyon, reported that a group of them scrambled some way down, and found that boulders they'd seen from the rim were not as they'd thought, the height of a man, but "taller than the great tower in Seville" (presumably the Giralda Tower, nearly 100m high).

We only stayed an hour or two. But before we left, from the rim I saw a trail, pale as chalk, winding down a huge slope beneath a cliff. There's something about a trail seen from far away. That thread snaking over the landscape – where does it go, who uses it, why does it seem so intimate with the land? And why does it arouse such an intense longing to follow it? An unknown path seems almost necessarily a metaphor. We like to conceive of life as a thread, after all, a path crossing unexpected terrain on its journey to another element. When the trail winds across empty desert, up and down huge hillsides – as in the Grand Canyon – it's all the more insistently allegorical.

There wasn't time to follow it, and I left with a nagging sense of opportunity lost, and that pale thread of a path still pulling at me.

It wasn't until last winter that I got to answer that pull. And the first thing I learned is that with the Grand Canyon, winter is the time to go. As the chief district ranger, John Evans, told me, "You'll more or less have the place to yourself." Although the canyon is a desert, it's like an oasis in winter – a place of peace, sequestered from the rest of the world. In three days of hiking I saw only two or three mule trains, each carrying baggage, not riders, and perhaps two dozen hikers.

Winter is cool, and cool is good for hiking. It's true there's snow on the trails, and long-moulded tongues of ice pounded into enamel-like smoothness by the mules that go up and down with supplies, but that's only on the highest reaches. Drop 500m from the rim and you'll probably be free of it. Sunlight becomes a blessing instead of a 50C curse when you step out of chill shade into some welcome warmth.

To experience the canyon, you have to leave the rim. The frustration aroused by the bigness, the grandness, on a rim-only visit becomes a liberation once you drop down. The modern world falls away. It's a trip not just out of the human realm, but into the deep geology of the earth. Layer upon layer of the planet's crust is revealed, stratum by stratum: the Toroweap limestone, the Coconino sandstone, the Redwall limestone, the Tonto Group; the Vishnu schist deep down, close to two billion years old, nearly half the total age of the planet – the stuff that is under our very feet as we go about our lives is laid bare here. And in the silence and stillness, in the solitude of the canyon in winter, it's all the more impressive.

Teddy Roosevelt said that all Americans should try to see it. He also declared: "We have gotten past the stage, my fellow citizens, when we are to be pardoned if we treat any part of our country as something to be skinned."

Alas, he had no idea what was coming. But the Grand Canyon has not yet been skinned. Though not for want of trying.

As I prepared to go, and talked to friends about the trip, I was amazed how many people knew the inner canyon well. One acquaintance told me he had spent 300 nights below the rim, falling just short of a lifetime's ambition of a full year. In a grocery store in Santa Fe, where I live, I got talking with a Grand Canyon-crazy runner who hikes from rim to rim in a single day several times a year. A woman in a coffee shop told me about the time a 10lb falling rock nearly knocked her off a trail. I began to get the feeling that the Grand Canyon is truly a national monument, analogous to the Lake District in its centrality to the nation's psyche. "Each man sees himself in the Grand Canyon," Carl Sandburg said. It's something all Americans share, and can take pride in.

This was all very well, but the canyon is a mile deep, and the trail itself about 10 miles long, and that translates to a very arduous walk, especially for an eight-year-old. By some arcane family algebra, it was the turn of Saul, our younger son, to come with me.

After an impossibly smooth two-hour ride in the vintage coaches of the Grand Canyon Railway from the town of Williams, Arizona, the nearest major settlement south of the canyon, we checked in at Bright Angel Lodge near the canyon rim, to reconfirm our bookings for Phantom Ranch, down in the bottom. The woman behind the desk glanced at my son and said: "I hope you're planning to leave immediately, if not sooner."

It was already 1pm, and most hikers set off in the morning.

My heart dropped. Saul is strong, fit as an Olympic athlete, indomitable as a Gaul, but still only eight. Was it crazy and cruel to ask him to walk down and then up a whole mile of elevation? What if, having got him down, he hurt himself, or his feisty spirit gave out? And what if my own legs failed me?

The fear amplified during the first spectacular mile of trail, where we had to pick our way precariously over ice. But then we were out on the spine of a ridge, the aptly nicknamed Ooh-Aah Point, that dropped precipitately to either side, and the ice was all melted away. Here, it wasn't so much about looking at a view as being in the midst of one.

As we gazed around us, two condors came gliding right over, so close we could hear the wind ruffling their feathers.

"Keep in the middle," I implored Saul, as he took to scampering along the parapet of rocks. Apparently, kids can't resist a parapet, no matter the drop beyond it.

I wouldn't want a creationist to misinterpret this, but I always find geology more or less unbelievable. Were these hundreds of square miles of limestone hundreds of feet deep truly formed by trillions of marine creatures dying? Could a river really carve out a gash this deep? But before the construction of the Glen Canyon Dam, in a single day the Colorado River used to carry away 380,000 tonnes or more of silt, enough to fill a train 25 miles long. Each day. A river this size is indeed an efficient grinding tool.

Below us, sweeping brown plateaux bulged as if they were soft upholstery. There were cliffs of blue, pink, orange, mauve, and deep purple bands of rock – the banners of God, as an early explorer said. True enough, the stark minerality of the desert always seems to arouse the inner mystic.

The scientist John Strong Newberry, part of an 1857 expedition to the canyon, said: "Nowhere on the earth's surface, so far as we know, are the secrets of its structure revealed as here."

After the cliffs of pale Coconino limestone, we descend the Redwall limestone, into a deep tub of crimson stone. Finally, at Skeleton Point, we catch the first glimpse of the river, thousands of feet below, announced by a distant roar.

A vast sweep of shadow is coming off the rim above, spreading over the Tonto plateau. We plunged in and out of the shade on the switchbacks. So far, we had seen just four people. Then, just after Tipoff Point, the path brought us to another dizzying corner, overlooking an ancient rusty amphitheatre of Tonto Group rock one way, while to the other, the air drops away to another sight of the Colorado River far, far below, clay-red, rippling, bloated. One of the two suspension bridges down there was visible, too. It all looked like a telephoto shot, the unfamiliar vertical distance baffling the eye.

Around 4pm, when we'd descended around 1,200m, deep in the echoing inner canyon, amid runnels and gullies of deep shadow, beneath shoulders of shale and scree, Saul got a kind of oxygen narcosis, skipping around, singing "Blue-blue-blue-blue" from Austin Powers, while my left knee went supersonic, screeching at me to please take one pace up instead of down. Then Saul discovered the echo deep in the billion-year-old rock. "Go away, echo!" he shouted vainly, again and again.

Endless new levels, new shears, shelves and tables to descend. Then all of a sudden, there was the bridge again. This time, we could see its individual railings, and as we approached, through a tunnel hewn straight through the rock, the thick, deep air beside the rushing river was like a balm. Whether it was the late afternoon light, the fatigue, the pain in my knee, or the relief of getting down, I found myself wallowing in a wonderful endorphin bath. The world went glassy. The canyon cliffs and trapezoids and pinnacles of rock all became resonant. I watched myself walk, as if the real me were a deep witness to my life, rather than the one who apparently lives it.

Down here, with the enormous Colorado River beside us, encased in the immense walls of the inner gorge, we passed the old settlement of Anasazi Indians who lived here 1,000 years ago. They planted corn and squash, and used nothing that didn't come from their immediate surroundings. It occurred to me that today it takes a whole afternoon on vertiginous trails to accomplish the reverse: to enter an environment without human imports. This is surely the kind of immersion a hiker seeks; this is why it felt like a pilgrimage to come here. It was good to reflect that if America has a heart, this just might be it.

By the time we reached Phantom Ranch, its own side canyon, Bright Angel Creek, was deep in chilly shade. On reaching the quiet huddle of stone and timber cabins under their grove of silvery cottonwoods, the trees tattered with old dry leaves, with a bunk waiting, and hot showers in the bathhouse, and the creek plashing by – I was flooded with relief. But even though we'd descended to 700m above sea level (from over 2,000m) it was still freezing.

When the ranch bell rang for dinner, some two dozen guests trooped from their cabins through the frigid dusk to the main lodge, where we quietly feasted on stew, corn bread and salad. We were from all over, all walks of life: a student from Quebec, a trucker from Kentucky, a fisherman from Alaska, a college student from New York, a woman in insurance, from Pennsylvania. All these trappings of people's lives seemed to fade in the context of this deep retreat from the world. We were just people, making the pilgrimage from cradle to grave.

At 8pm the dining room turns into a kind of mess hall. People sit around playing cards, or Trivial Pursuit, drinking wine or beer, and the counter opens for the sale of odds and ends. On a shelf sits the box for river mail, where letters wait for rafters coming downstream.

It was 2am when a cry pierced the peace in our cabin: "I feel sick, Daddy." No sooner had I sprung from my bunk to fetch the rubbish bin than Saul was hunched over it, retching. By 6am he was hot with fever. It had happened: stuck at the apex of a mile-high inverse mountain in winter, with a sick child.

At first light Bright Angel Creek was chalky, vague. Then distant bluffs of red stone got picked out by the sun, and more and more bright geometries emerged. While I was wondering what to do, rows of Easter Island-esque monoliths along the top of a cliff turned bright, and when the early sun struck the high outcrops, I could see how they got their Egyptian and Hindi names. They did look like sphinxes and Oriental temples. At 8am I went to the lodge and asked if they had a thermometer. They radioed down to the ranger station, and 10 minutes later Eston Littleboy Jones, a ranger equipped with a holstered automatic pistol and a Taser gun, was tending to my son.

Saul's eyes lit up at the sight of the guns. A quick check-up, and he was bouncing back. By 11am he was insisting we walk the Overlook Trail mentioned by Eston, one-and-a-half miles up to an outcrop overhanging the creek, then the River Loop Trail. Apparently, it was a swift-moving stomach bug.

My legs were stiff as stilts. It was as if, never having been near a Stairmaster, I had decided to spend all of yesterday on one. But hiking seems to ease them.

From one of the two suspension bridges we stared down at the river.

"It looks like they're fighting a war," Saul said of the white waves. "Fighting to get up the river." The frothing eddies did seem to be struggling with the current. Two plumes of ripples curved into one central stream like trails of smoke sucked into a flue. The canyon walls created a constantly changing concertina effect with volume. There was a great bow of a pebble beach, except the pebbles were the size of cars. It's a landscape from The Lord of the Rings, with a perilous cliff path to match. Any minute our way would be blocked by an orc.

The next day we made the climb back up the Bright Angel Trail. Like the Kaibab Trail, this was also built for mules, having first been a Native American trail to the creek at Indian Gardens, half-way up. Mule trails are good for hikers. The beasts won't put up with anything too steep. The trail makes its way up cliffs in endless switchbacks.

Rows of flying buttresses, a soaring ship's prow throwing a huge flag of shadow across a cliff, a forbidding wall of masonry half a mile above us: the views never stopped coming. Way above, on the whitish cliffs just under the rim, something was winking. Could it be the windows of El Tovar, the old hotel where we'll be spending the night? Along the climb at Devil's Corkscrew, a chain of little waterfalls has carved out smooth dark basins in the rock. Again and again it struck me how perfect the temperature is for hiking. Through a grove of willow the stream flashed by, icy cold.

On that day we passed five hikers. Once again, it was just us and the canyon. And the circling condors overhead.

On the last two miles, stalactites of milky ice hung beside the trail. Then solid grey snow was underfoot, like lacquer, impregnated with dust, slowing us right down. As we stood still waiting to see if we could catch the sound of wind in the feathers of a condor gliding by, we heard from up above the deep gurgle of the first motorbike. After three days away from carbon culture, the modern world seemed like Thunderdome now.

Finally, we slumped into El Tovar, the oldest Grand Canyon hotel, with its fireplaces of stone blocks and masses of dark timber, a perfect hiker's rest.

The truth is, when I pulled into the Grand Canyon years before, I didn't even comprehend that it was a canyon. It was such a vast landscape it seemed it might go on in pinnacles and gulfs for hundreds of miles. But once you've been down into it, you know what it is. You understand. At least a little. And the mere thought of being disappointed by it? I'm positively looking forward to Judgment Day.

© 2009 New York Times News Service

Essentials

Getting there

Virgin Holidays (0844 557 3859; virginholidays.co.uk) offers a seven-night fly-drive to Las Vegas from £499, including flights and car hire. The historic railway (+1 303 843 8724; thetrain.com) from Williams takes two-and-a quarter hours. Returns from $70 adults, $40 children.

Where to stay

The Grand Canyon Railway Hotel in Williams (+1 800 843 8724; thetrain.com) is not an atmospheric old railway edifice but a comfortable, modern hotel, with doubles from $169. El Tovar (+1 888 297 2757; grandcanyonlodges.com)has been open since 1905 and shouldn't be missed. Doubles from $174. Phantom Ranch (details as El Tovar) is a collection of cabins in the bottom of the canyon. Dorm beds from $42. Bright Angel Lodge (details as El Tovar) is a 1935 timber warren, full of charm, with doubles from $90. Availability at hotels in the canyon can be a problem, but the village of Tusayan, a mile outside the park, usually has vacancies. Doubles at Red Feather Lodge (+1 866 561 2425; redfeatherlodge.com) cost from $73.

MORE INFORMATION

The National Park Service's website (nps.gov/grca) is helpful, as is grandcanyonlodges.com. .