Uniformed flunkies are busy polishing the windows as taxis draw up to five-star turn-of-the-century Swiss hotels. Preparations are under way for the World Economic Forum (WEF) in Davos – first held here 40 years ago, arriving again in a week's time – and it's a curious collision of worlds. At breakfast, an elderly American is discussing a theory on the developing world with a colleague while families in ski outfits eat at the next table.
Outside the conference centre, winter-sports enthusiasts and delegates part company. The skiers pile into the small cabins of the Parsennbahn, a railway that climbs alongside the downhill slopes. Romanesque arches and continuously whirring wheels give it the feel of a ghost train. From the summit you can ski into the maze of pistes that run through the forest into Klosters and its surrounding villages, but this is not where I enjoyed my best day's skiing in the resort. Nor was it in the Rinerhorn or Jakobshorn areas, nor in the much smaller areas of the Madrisa and Pischa mountains – both popular with beginners.
Looking down towards the town and its 700-year-old church with landmark twisted spire, I drank in the network of vein-like rivers and valleys cutting through the plateaux that form yet another world in Davos – cross-country skiing. Forsaking the lifts, I made my way to where tall spruces separated Jugendstil (art nouveau) town houses. Here I found the start of the loipe – cross-country trails – and Hoffmänner Sport, where the staff were happy to rent me the appropriate boots and skis.
Gliding alongside the Landwasser river, I became engulfed in a cloud of mist lingering above it. The vapour rose on this bright and frosty morning to join columns of wood smoke from farmstead chimneys. I left the riverside park, with its curiously redundant benches and birches laden with snow. Further on, barnyard smells joined the mix.
It is a world little changed from the Davos that Sir Arthur Conan Doyle knew. In 1894, the creator of Sherlock Holmes sat with his wife, Touie, who was recovering from tuberculosis, and planned a skiing expedition. He had spent weeks by her bedside and was now about to set off on an adventure that would popularise downhill skiing in the Alps. In those days, there was no distinction between downhill and cross-country skiing, while Conan Doyle had to contend with skis he described as "the most capricious things upon earth".
A first-time cross-country skier will almost certainly feel the same way. The skis are long, spindly and detached from your heel. For the first few steps you will struggle to discover the use of your newly extended legs. At least in Davos you can follow tramlines in the snow (carved with a device dragged from the back of a snowmobile).
After a while, you'll get the hang of walking on the skis, and many people are happy to do just that, but to experience the full joy of cross-country skiing you should develop your technique, best achieved by booking a lesson. Why do you need instruction? You will find that as soon as you try to get up some speed your skis will start slipping backwards. There's a ribbed bottom to the part of your ski under your foot, allowing it to grip when you put your weight on it, while throwing the other ski forward. In the Nordic countries the same effect is achieved by putting wax on the section underfoot.
Nonetheless, it is difficult to shift your weight in this way and this is where most beginners give up. There is no magic answer – it simply comes with practice. It's a question of trying to get it right more times than not. If you stick with it and have a good instructor you will learn to stop walking on your skis after a few days and really start gliding, using your poles in an alternating motion.
Soon you will find that you can move faster than you can run, but with the benefit of cross-country skiing being far kinder to your joints. The more adventurous might even want to try the modern "skating" technique, with your skis forming a V-shape.
Feeling daring, I followed one of the steepest of 75km of immaculately maintained trails along the Flüela Pass, criss-crossing the stream over wooden bridges until I returned on a speedy and slightly terrifying downhill section.
Steep slopes aside, you can go cross-country skiing at any age without any real fear of injury. And that, perhaps, is why world leaders all come to Davos once a year. You might wonder why the Klaus Schwab, WEF's chairman, decided to hold the conference in a ski resort. The answer, locals will confide, is that Schwab, the forum's founder, picked the town for the congress soon after he bought a holiday home here to come cross-country skiing.
The key to pleasurable cross-country skiing comes from choosing your location carefully. Having become accustomed to gliding only through the wonderful wildernesses of the Nordic countries and Canada, I had been a little sceptical of venturing into new territory. In most Alpine resorts, the cross-country skiing amounts to little more than doing laps in a field at the bottom of the lifts.
Here, there were gentle trails running from village to village between the dramatic peaks of the canton. What's more, Switzerland's ever-reliable rail service allows you to explore new trails far away, or catch a lift back if you are feeling tired.
And whatever your technique is like, you will have no smoother ride than when following the loipe back through the valleys, holding your featherlight skis on the train.
* The most convenient airport is Zürich. The train (changing at Landquart) takes under three hours. From Basel, the journey is just over three hours long.
* Headwater (01606 720199; headwater.com) offers a seven-night stay at the 19th-century, four-star Hotel Meierhof, which has an indoor pool and spa, from £1,334 half board, including flights from Heathrow, with the option of non-stop flights with Swiss from Birmingham, Manchester, Gatwick or London City, rail transfers, travel on local transport, equipment (boots, poles and skis), plus three two-hour lessons with a cross-country instructor.