When a skier is stock-still halfway down a piste, it usually means they are frozen with fear. They are unlikely to have stopped to "listen to the whispers of the mountain" – unless they are on the Paradiso piste in Corviglia, just above St Moritz, Switzerland. Welcome to the world's first yoga piste. Only in St Moritz, right? You could be forgiven for dismissing ski yoga as the latest gimmick for people with more money than sense (and there are certainly plenty of those here).

Holidays that combine skiing and yoga classes are nothing new, but doing yoga on skis takes the concept a step further. The Swiss yoga piste, also known as the chill-out slope, was dreamed up by Sabrina Nussbaum, a local ski instructor and yoga teacher. She noticed that her fellow ski instructors were taking up yoga after suffering knee and back injuries, and thought that everyone could benefit from skiing in a more "yogic" way.

Sabrina has selected four particularly scenic sites at which to do eight asanas (yoga postures). The slope is a red run and the sites themselves are off-piste, so beginners would struggle to reach them, but really the postures can be done anywhere on the mountain. You can pick up a "Yoga on Snow" leaflet at the surrounding ski lifts and follow the routine for free.

Or you can book a half- or full-day lesson with Sabrina or her colleague, Priska Hotz, both from the Suvretta Snowsports School – some clients book a week, or even a whole month, of ski yoga. I spent a day with Sabrina, which included about six hours on the slopes, plus a 90-minute yoga class in the evening. Before I started, I was stiff and sore from the previous day's skiing, my first in two years. I was also a little nervous, because I seemed to have forgotten all my technique.

We started, appropriately, with a tadasana (mountain pose). I dropped my poles, stood up straight and closed my eyes. Sabrina told me to relax my feet and be aware of the mountain beneath them. It may have been the fresh air and sunshine, or the altitude, but I immediately felt relaxed and happy. After each pose, we skied for a while, applying the principles of the asana to the skiing. So first I tried to keep my feet flat and grounded, lifting my toes during difficult sections, rather than scrunching them up tight. It was incredible how much more control I had over my skis. Changing one simple thing, rather than trying to remember a dozen rules, was a revelation.

We stopped on top of an easy run to work on prana, or life force. This involved covering my ears and concentrating on my breathing. We skied down with our ears still covered, focusing on breathing calmly – quite difficult when you can't hear other skiers whizzing up behind you. We worked on breathing only through the nose for wide, gentle turns, or using "breath of fire" (a powerful, rhythmic pattern) for short, fast turns. The most useful exercise was remembering to exhale during fast or stressful moments, rather than holding the breath and tensing up.

At lunchtimes, an array of expensive slopeside restaurants cater to the resort's super-wealthy clientele. La Marmite, for example, which specialises in caviar and truffles and, at 2,486m, is Europe's highest gourmet restaurant – with prices to match. But we skied down to Clavatasch, a "hidden" restaurant near St Moritz's village neighbour, Celerina. The wooden building is a former cowshed and has a tiny kitchen serving cheap, local specialities such as barley soup – a tasty but suitably healthy dish. (It doesn't have a website – ask around for directions, though even some locals I spoke to had never heard of it.) Braulio, a herbal alpine liqueur, is a warming digestif that fires you up for an afternoon's skiing.

Equally, St Moritz Dorf (the upper, main part of town) is full of designer shops, five-star hotels and exclusive restaurants. But St Moritz Bad, down by the lake, is a better choice for a cheaper trip. I was staying there at Hotel Piz, a friendly place with a great pizzeria and a lively bar full of locals watching football. Across the road is Veltlinerkeller, a rustic restaurant that serves the carb-heavy dishes typical of the region, such as pizzoccheri – buckwheat pasta ribbons with swiss chard, potato and more cheese than you would ordinarily eat in a month. It is great fuel for all the activities available in St Moritz, the birthplace of winter sports tourism. I tried snowshoeing and cross-country skiing, and you can channel your inner Winter Olympian with bobsleigh, skeleton, curling and ice-skating.

Back on the slopes, we found a sheltered, sunny spot to do some sun salutations – a good way to warm up – then returned to the yoga piste for more skiing and assorted asanas: the powerful warrior pose; the muscle-loosening triangle stretch and forward bend; the tree pose for balance.

Whereas the previous day I had felt stressed and tired after a few hours, now I was calm and energised – I didn't want to stop. But it was time for savasana, or relaxation, at a beautiful spot on the edge of the slope, overlooking a string of lakes in the Engadin valley. I lay on my back, feeling the sun on my face and my body supported by the fresh snow, listening to the swoosh of skiers and the whispered wind. Yoga on snow didn't feel like a gimmick – it felt like a whole different way of skiing.

• Accommodation was provided by Hotel Piz (+41 81 832 11 11, piz-stmoritz.ch, doubles from £128 a night B&B). Flights were provided by Swiss Air (swiss.com) which flies from Heathrow, London City, Birmingham and Manchester to Zurich from £132 return. Train travel was provided by Swiss Railways: a return ticket from the airport to any Swiss destination costs £96 (swisstravelsystem.co.uk). Ski yoga tuition costs from £60 for a half day, engadin.stmoritz.ch