St. Moritz sells itself as the top of the world, and it did invent something: the Alpine winter holiday. The story goes that in 1864 the hotelier Johannes Badrutt bet his English summer guests they'd be sitting on his terrace in shirtsleeves in winter, and they went home brown. It's a great story and it can't be proven. The hotel's guest list says the first Englishman to spend a winter in St. Moritz was Arthur Strettell, a tuberculosis patient who stayed from July 1866 to June 1867. What is solid: the town hosted the Winter Olympics in 1928 and 1948, built the world's last natural-ice bob run, and still races horses on a frozen lake.
It is two places at once. There's the glossy town, with Via Serlas shop windows, five-star hotels and prices to match, and there's the Engadin behind it: three big mountains, nine ski areas on one pass, frozen lakes and a railway to Italy. Be honest about the cost, because this is one of the dearest ski bases in the Alps. The good news is a fixed-price pass sold with the hotel (CHF 55 a day) and villages a few minutes away by train. Five days is right because each mountain deserves its own day and the Bernina train deserves a fourth.
The plan: Corviglia on day one, Corvatsch and Furtschellas on day two, Diavolezza and Lagalb on day three, the Bernina line to Tirano in Italy on day four, and a day in St. Moritz itself on day five with the Cresta Run, the Segantini Museum, the lake and Friday night skiing at Corvatsch. Start on a Monday: the railway says Monday to Thursday are quieter on the Bernina line, Thursday is then a clean train day, and Friday is the one night of the week with Snow Night. If you're coming from the Matterhorn side, the Glacier Express links Zermatt and St. Moritz in a day. For everything else about the country, see Switzerland.