Rarely can the colour white have seemed such an interloper. It has slithered and slathered itself over every available flat surface, clinging to cracks and lying on ledges. True, the darker hues usually associated with this scene – hazy pink, warm red, solid brown, sunset orange – are all visible. But their ruddy demeanour is partially hidden by this pale shroud.
Popular imagination says that the Grand Canyon should not look like this – its cragginess softened by snow. The classic image is rather harder: a geological scar – 277 miles long, up to 18 miles wide, 6,000ft deep – where two billion years of Earth's history are flaunted in natural erosion; a place indelibly linked to heat and dryness, all harsh sun and rattlesnake hiss; the great divide that marks the most indisputable of all American state lines as it dissects Nevada and Arizona. Alone, the Colorado River soothes the area's parched tongue below.
And yet, I am not exactly surprised. The idea of glimpsing one of the world's most iconic landmarks in its winter disguise seems a possibility by the time I reach Flagstaff, heavy frost garnishing the fringes of Interstate 17, hail punching angrily at the windscreen. The real shock is the speed of transition, Phoenix's desert setting – which effortlessly pushes the temperature in the Arizona capital into the 70s, even in February – surrendering meekly to a chillier realm as I forge north, the mercury dropping 40 degrees in 100 miles.
This is down to Arizona's diverse geography. Perceived as an expanse of sand and cacti (which it is in its southern third, where the Sonoran Desert declines to halt at the Mexican border), America's sixth largest state also proffers the elevated scrub of the Colorado Plateau in its north-east corner, and high-rise terrain where the Mogollon Rim escarpment spans its midriff. The Grand Canyon, caught between plateau and peaks in the north-west of the state, has to cope with wild seasonal mood swings – whatever its postcards suggest.
So much becomes clear as I continue up Route 64, the wind howling in protest. Off to the east, the San Francisco Peaks prod the sky, their tallest member – the 12,633ft beast that is Humphreys Peak – so titanic that you can ski on its slopes at the Arizona Snowbowl.
Beyond the small town of Tusayan, gates guard the entrance to Grand Canyon National Park. "I have to tell you, the visibility isn't good," says the park official as he takes my $25 (£17) admission fee. He has a point – although he is entirely missing another. Many people have seen this natural wonder in its summer finery, even if only in photos. But it is a rare privilege to catch sight of it when the worst of the weather is doing its best to repel you.
Three miles further on, mist and cloud clog up the maw of the canyon beneath Yavapai Point. But every couple of minutes, the wind tugs at the fog, the vapours part, and those sheer walls of stone are revealed in the gap. All around, the snow is mounting a campaign of conquest, weighing down bushes, masking pathways and supplying an extra note of treachery to the rocks at the lip of the abyss. It is as if someone has gouged a slice from a giant Christmas cake, cutting through the icing to uncover the fruit of the matter within.
Not everybody is impressed. A few yards away, an American family is surveying the murkiness with suspicion, a teenage son registering bemusement in shrugs and sighs. A park ranger – the voice of pragmatism – is standing alongside, explaining the situation.
"We're at 7,200ft," he nods, face semi-lost under a furry hat. "We can have snow at any time from November to June. Last year, we had it in May. It gets pretty cold up here."
He is correct on all scores, but especially the last one – so I retreat into the refuge of the Yavapai Point Museum. Perched precariously on the edge of the drop, this 1928 structure delivers brief insight into the canyon's formation, but is chiefly of interest for the view it provides. In the far corner, a gilded picture frame of the type you find in the Louvre has been fixed to a window – an effective way of emphasising the majesty of the panorama.
At the top, a quote from Theodore Roosevelt – one of the key players in the creation of the national park – has been glued to the glass. "Do nothing to mar its grandeur, for the ages have been at work on it, and man cannot improve it," he says in sepia. "Keep it for your children, your children's children and all who come after you." Perhaps the 26th US president is watching, because, as I peer through the pane, the curtains of cloud open once more.
When I depart, I take the eastbound stretch of Route 64 – an indirect way of venturing back to "civilisation" that traces the South Rim for 30 miles of precipice coils and loops.
But before I turn off, I pass the station, where the carriages of the Grand Canyon Railway (the tourist service that runs 60 miles from Williams) are idling – the picture made all the prettier by the definition that the snow gives to the tracks, showcasing them as slick black parallel curves.
As the train leaves, its horn-toots are muffled by swirling flakes, making it sound curiously forlorn. My mood, as I drive in the opposite direction, is anything but.
The only non-stop flights from the UK to Arizona are with British Airways (0844 493 0787; ba.com) from Heathrow to Phoenix. Other airlines – including Delta, United and US Airways – offer one-stop links from a range of UK airports via their hubs.
Red Feather Lodge, 300 State Route 64, Tusayan (001 928 638 2414; redfeatherlodge.com). Doubles from $76 (£51), room only.
Grand Canyon National Park (001 928 638 7888; nps.gov/grca): $25 (£17).
Arizona Snowbowl (001 928 779 1951; arizona snowbowl.com): one-day pass $53 (£35).
America As You Like It (020-8742 8299; americaasyoulikeit.com) does a 15-night tour (Los Angeles, Las Vegas, Utah national parks, Grand Canyon, Scottsdale, Tuscon) that features two nights at the Grand Canyon. From £1,040 per person with flights, car hire and hotels.
Arizona Office of Tourism: arizonaguide.com