It’s like taking a starving man to the best restaurant ever and not letting them eat,” says Louis, shoulders hunched, scowling at the mint-white mountain peaks. Outside St Moritz train station, lights twinkle, snow begins to fall and everywhere is soft, crystalline white. It looks magical, yet it’s torture for one of us. I should have known that taking a ski addict to Switzerland for a no-ski break would be problematic, especially if the ski addict in question happens to be my temperamental teenage son.

“You knew the deal before we came. It’s hardly a deprivation,” I say, watching liveried chauffeurs holding tiny gold placards bearing names: Madame Petrov, Monsieur Felipe. Daimlers purr, waiting to whisk guests to opulent hotels further up the mountain

It wasn’t my intention to drop in on the Alpine playground of the super rich. I wanted to head straight for La Chaux-de-Fonds, the city designed by watch-makers and much admired by Karl Marx, via one of Europe’s most scenic rail trips, the Glacier Express. But in the spirit of balance and contrast, first we stay at one of St Moritz’s oldest hotels, the Kulm. In its fin-de-siecle foyer, chandeliers sparkle, log fires blaze and It girls drip in Fendi fur. It is like walking into the back pages of Hola!

Facebook Twitter Pinterest Ice magic … skating at Kulm Hotel

“We have a six-course tasting menu booked for you in the grand restaurant for 7pm,” says the lady at reception. My son Louis is perkier by the minute. Strangely his mood darkens when we are shown our room, complete with wrap around views of the Alps.

“I can’t believe it,” he fumes, pacing the marbled bathroom. “People have been living like this all along and I never knew. Now I can’t enjoy anywhere else.”

“And that’s the problem with coming to places like this,” I say. “You feel either moral outrage or envy. Neither makes you happy. It’s better just not to know.” But Louis isn’t listening. He is distracted by the in-house video on the TV. “Mum, look, you can hire a mountain for a day. It’s only £4,000. Can we come back?”

At supper, the waiter hovers while Louis eyes up the wine menu where bottles start at around £75. “I know it’s not a question you hear very often,” I say. “But what’s your cheapest glass of house red?” “House?” the waiter repeats, baffled.

The next morning, we head for the ice-skating rink, owned by the Kulm but open to the public. My instructor is charming and patient, holding my hands while I grit my teeth and try to forget about the last time I went ice skating 20 years ago and broke my ankle. She offers to take Louis nighttime skiing – a Friday tradition where for less than £20 you can enjoy Switzerland’s longest floodlit slope till 1am. He’s thrilled to get the chance to ski while I enjoy the outdoor infinity pool in peace. Later in reception, I hear an over-confident English accent: “My son is still on the slopes. I’m afraid we’ll be a little late for the country club.” I’m horrified to realise it is me. Time to go, before I start enquiring about mountain rentals.

Early next morning, we board the Glacier Express, the world’s slowest express train that has been running between St Moritz and Zermatt since 1930. It snows heavily the day we travel and much of the time we emerge from the darkness of each tunnel (there are 91 of them) into blinding white fog. But when it does clear, the scenery is spectacular. We enjoy a three-course lunch at our table as the train carves its way through the Oberalp Pass (2,033 metres above sea level) with its glaciers and peaks, then on through the Nikolai Valley, the deepest in Switzerland, arriving at Zermatt eight hours later. The next morning we board a train to La Chaux-de-Fonds, in the Jura mountains, and close to the French border.

Facebook Twitter Pinterest Glass houses … art nouveau balconies in La Chaux-de-Fonds. Photograph: Ernst Wrba/Alamy

If there is anywhere in Europe, let alone Switzerland, that is less like St Moritz in spirit, it’s hard to think of it. While St Moritz’s raison d’être is leisure for the super rich, La Chaux-de-Fonds is its polar opposite, created as a socialist antidote to all that glitz and privilege. Home of modern watch-making, the town prized industry and enterprise above all else. In 1794 a fire destroyed most of the buildings and, inspired by the radicalism of the French revolution, it was redesigned by the workers for the workers. Equality was built into the new city brick by brick. They chose not to have a civic centre given over to grand squares and palaces where the elite could parade their wealth and the poor would feel excluded.

The city is built in a series of grids, its layout like a chess board; streets were designed so workers and managers lived in close proximity, next to their workshops, with no neighbourhoods for the rich and ghettos for the poor. The boulevards are wide, allowing light to pour into the workshops so the watch-makers could work more efficiently. As a social experiment it was a resounding success; Marx described the town as “la grande manufacture” in Das Kapital. The craft of watch-making thrived and prospered well into the 20th century, surviving the quartz revolution of the 1970s – even today La Chaux-de-Fonds is home to the workshops or headquarters of Rolex, Patek Philippe, Zenith, Tissot and Omega, many of which were founded here.

Facebook Twitter Pinterest Face time … the International Clock-Making Museum, La-Chaux-de-Fonds. Photograph: Getty Images

The city is also home to the granddaddy of modernism, Le Corbusier, born here in 1887. In a snowy suburb overlooking the town, La Maison Blanche is a modernist gem built in 1912, and all the values that inspired the town are here in his design. Open-plan spaces for work as well as living, floor-to-ceiling windows so each room is flooded with light and, above all, the idea that everyone should be able to enjoy where they live. That night we stay at Grand Hôtel Les Endroits, a hotel on the edge of town where we we have our best meal so far, the food more French than Swiss, with shaved truffles baked with potatoes and cream, followed by chocolate patisserie.

Our final morning is spent at a watch tutorial where, with the help of watch-maker Sebastian, a powerful microscope and some tweezers, we try to attach both watch hands to its face. After an hour of intense concentration, we manage to assemble a watch that keeps time. “Satisfying work isn’t it?” says Sebastian, as Louis tries it on his wrist. “I guess,” he says, studying it. “So how much would it cost to take it home?”

Way to go

The trip was provided by myswitzerland.com, with flights with Swiss, from £67 one way. The Swiss Travel Pass offers unlimited travel and includes a museum pass; prices from £171. To book the Glacier Express go to glacierexpress.ch

Browse The Guardian’s selection of some of the world’s best rail journeys on the Guardian Holidays website

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