These are accessed via a 10-minute cable car ride that whisks you up onto the plateau, where the runs stretch up to a snow-secure 2700m.
Not only is Leukerbad a lot quieter than its better-known neighbours, it's also a lot smaller - with just 50km of skiable terrain spread across 18 runs.
However, all that was yet to come. Because first I had a spa appointment to attend - or rather a spa "breakfast".
I wasn't quite sure what to expect from this. Would I be eating toast while sweating it out in the steam room? Or perhaps the food bit would come afterwards - once I'd had a chance to detox and towel down? In fact, within seconds of launching myself into the al fresco thermal pool, a plate of breads and cured meats emerged through the thick steam, bobbing towards me on a rustic wooden board.
It was certainly strange, sitting back in the warm waters, helping myself to a floating plate of cold cuts while watching the early morning sun rise over the surrounding cliffs - but I felt surprisingly relaxed. This was possibly down to the accompanying glass of prosecco, which made me forget all about the other (thankfully swimsuited) bathers bobbing around nearby.
The weekly spa breakfasts, held at the Burgerbad in the centre of town, are just one of the treatments on offer here. Wellness centres are common in European ski resorts, but it's the scale and heritage of Leukerbad's facilities that make them unique.
People have been visiting the town to take to the waters since the 16th century, making it the oldest spa town in the Alps. It's also the largest, with 30 pools spread around the resort offering all kinds of bathing experiences.
At the Lindner spa, for example, you can enjoy a soak while watching a movie on the big screen; or bask in the bubbles under the silvery glow of a full moon.
There are treatments on offer here to satisfy even the most bizarre penchant, but the one that sounded most intriguing was the "Roman-Irish" night. Held once every few weeks, you get to dress up in a toga and enjoy a Roman-style feast before disrobing for an elaborate series of scrubs, baths and back-rubs. Sadly, my visit didn't coincide with this extraordinary event this time.
Back at the Burgerbad, my fingers were turning wrinkly - and I'd run out of prosecco. It was time to hit the slopes. Half an hour later, I was shaking hands with my guide, Rachel, at the top of the main gondola.
If, like me, you believe that quality is more important than quantity when it comes to piste mileage, then you'll love it here. A half-day session with Rachel was enough to cover most of the runs, and we spent a relaxed morning cruising a blend of reds and blues - stopping every so often to soak up the view.
Even by Swiss standards the scenery here is spectacular. From the top of the Torrenthorn lift it seemed as though we had the whole of the Alps spread out before us. I'm generally hopeless at spotting famous peaks, but there was no mistaking the iconic tip of the mighty Matterhorn. Just to its right was another Alpine giant, the Weisshorn, topping out at over 4500m - and way off in the distance, the daddy of them all: Mont Blanc.
The terrain here is reassuringly mellow, mostly made up of intermediate runs, and after a leisurely lunch at an on-slope eatery, Briand, I headed back to the village for my next spa treatment. This time there was no getting out of it, nudity was compulsory.
The only way ahead was to embrace it. So amid the Romanesque backdrop of the Lindner spa, which is all decadent arches and lush greenery, I spent an indulgent two hours being scrubbed, soaped and covered in mud - minus the toga.
It was all part of an elaborate ritual of 11 treatments, designed to wash away stress as the Romans did - climaxing with a particularly chilly moment in the frigidarium.
By this point, though, I was finally at peace with the concept of bearing all in front of total strangers.
Further information: See myswitzerland.com.
- INDEPENDENT