Some mountains you photograph; the Matterhorn photographs you, rearranging every picture you take in Zermatt around its crooked pyramid. This route runs the length of the Valais from Lake Geneva, climbs to Zermatt for a few days under that mountain, then rides the most famous railway line in the Alps east over the Oberalp Pass to the Engadine. It is Switzerland's glacier country end to end, and with a couple of tricks it is survivable on a backpacker budget.
Lake Geneva to the mountains
Start in Geneva and take the train along the lake to Montreux, an hour of vineyards stacked above blue water. Montreux is worth an afternoon and a walk to Chillon Castle on its rock in the lake, about 15 francs entry. From there the main line runs up the Rhone valley to Visp, where the narrow-gauge Matterhorn Gotthard Bahn hauls itself up a gorge to car-free Zermatt; Geneva to Zermatt totals about three hours. Buy the Half Fare Card, roughly 120 francs, before any of this; every train, bus and cable car in this itinerary drops to half price and it will save you multiples of its cost.
Zermatt on the cheap
Zermatt is a resort with resort prices, but backpackers have workarounds. The youth hostel and a couple of independent dorms run 50 to 70 francs with breakfast; booking weeks ahead matters in July and August. Self-cater from the Coop by the station. Then hike, because the best of Zermatt is free. The classic is the Five Lakes Walk above Sunnegga, where the Stellisee gives you the mirrored Matterhorn shot on calm mornings. Stronger legs should take the trail toward the Hornli hut side of the mountain or up the Gornergrat line's path, walking down from whichever station your budget reaches. If you ride one big lift, make it the Gornergrat railway at dawn, half price with your card: the platform at 3,089 metres looks over the second-longest glacier in the Alps, the Gorner, pouring grey and cracked beneath Monte Rosa. Keep an eye out for black-nosed Valais sheep, absurd and friendly, grazing the high meadows.
Riding the Glacier Express line without the price tag
The Glacier Express markets itself as the slowest express train in the world, eight hours from Zermatt to St. Moritz through 91 tunnels and across 291 bridges. The panoramic train requires a seat reservation of about 49 francs on top of the fare. The trick locals will tell you: ordinary regional trains run the identical track for the normal fare with no reservation, windows that actually open, and the freedom to break the journey. We hopped off at Andermatt, a laid-back mountain crossroads at 1,440 metres, stayed a night in a cheap gasthaus, then continued over the Oberalp Pass at 2,033 metres, where the train runs above the treeline past the source of the Rhine.
The Engadine finish
The final stretch drops through the Rhine gorge, a pale limestone canyon the Swiss call their little Grand Canyon, then climbs into the Engadine to St. Moritz at 1,822 metres. The town itself is furs and watch boutiques, but the valley around it is superb walking country: lakes strung like beads, larch forests, and the Bernina peaks hanging above. Dorms in nearby Pontresina and the St. Moritz hostel keep it affordable, and your Half Fare Card works on the Bernina line toward Italy if you cannot stop riding trains, which by this point you cannot.
Numbers and timing
Budget 90 to 110 francs a day. July to September for hiking; late September paints the Engadine larches gold. Reserve Zermatt beds early, carry supermarket food on every train, and sit on the right-hand side leaving Zermatt for the valley views.