Follow in the footsteps of Kate Humble and Planet Earth II at America's greatest National Park

That harsh winter also made two appearances in Planet Earth II. Remember the bobcat that prowled among snow-clad mountains, diving whiskers-first into drifts? Those peaks were the Yellowstone Rockies and the balmy watering hole where the bobcat finally struck lucky was fed by one of the park’s volcanic hot springs.

In the grasslands episode, a herd of bison lumbered through a thick blanket of snow in Yellowstone and a fox ensnared its dinner – a doomed vole.

The hungry fox in the grasslands episode of Planet Earth II

Yellowstone, America’s most famous national park, was also the world’s first. In 1872, an act of Congress decreed that 3,500 square miles near the headwaters of the Yellowstone River, be “set apart as a public park or pleasuring-ground for the benefit and enjoyment of the people”. Nearly a century and a half later, four million visitors flock there every year to see its bubbling mud pots and roaring geysers, including the iconic “Old Faithful” spurting every 90 minutes or so.

Yellowstone also boasts its own 20-mile-long Grand Canyon, with spectacular pink and yellow rock and a waterfall over twice the size of Niagara Falls, while its huge azure lake (see main pictured above) is a breathtaking sight when the vast surface reflects the sky and the Rockies.

Then there’s the fauna. Yellowstone is one of the best places in the US to see wildlife in its natural habitat, earning it the nickname “the American Serengeti”. Its best-known residents are grizzlies and black bears, but two decades ago, 40 wolves were reintroduced and there are now over 100 in the park. They’ve had a positive impact on the ecosystem because wolves prey on deer and coyotes, and fewer of those means more beavers, reptiles, rabbits and eagles.

The best time to spy a bear or wolf is at dawn or dusk in Yellowstone’s broad valleys, where you can also see mule deer, bison, moose, bighorn sheep and pronghorns – the second-fastest land mammal in the world after the cheetah.

The majority of people visit the park between May and September but – as those stunning sequences in Planet Earth II illustrate – there’s something magical about the low season when the park is snowbound.

“It’s a wonderful place to go in the winter,” says producer Justin Anderson, who oversaw the mountains episode. “It’s beautiful and super-quiet. It’s also one of the best times to see the animals because they all congregate at the volcanic hotspots. They’re pretty sensible. They don’t stand out in the snow; they hang around where it’s a bit warmer.”

A bobcat dines at a balmy watering hole in the mountains episode of Planet Earth II

Holidaymakers should be prepared for snow even in autumn and spring when the temperature can fall to minus 20 degrees. If you don't fancy going it alone, there are organised tours, ranging from skiing and snowshoe expeditions to trips to the Grand Canyon’s waterfalls, which freeze mid-cascade.

The park’s campsites and lodges are only open during the summer months, but from mid-December through to February you can book a cabin at the Old Faithful Snow Lodge – the Scandi-style sibling of the park’s oldest and most popular lodge, the Old Faithful Inn.

If you really want to escape the crowds, Yellowstone Expeditions run a yurt camp near the Grand Canyon – miles away from any other human habitation – from late December to March. There’s a snowcoach shuttle from the town of West Yellowstone, but after that it’s cross-country skis and snowshoes all the way. At $1,100 for three nights, it’s not cheap, but guests stay in private heated huts that have access to a sauna, hot showers and a dining yurt where communal meals are served.

Yellowstone begins on Tuesday 3 January on BBC2 at 9pm, and continues on 4 and 5 January