Switzerland's trains are expensive if you buy point-to-point tickets. Buy a four-day Swiss Flexi Pass through Rail Europe (raileurope.com), however, and you can do the entire Zurich-Zermatt-Andermatt-Engelberg-Zurich loop for $196. If you travel in a group of two or more, you save 15 percent; if you're under 26, you save 25 percent. Rail Europe can take care of seat reservations-mandatory on the Glacier Express (glacierexpress.ch). They also sell you vouchers ($15/bag) for the Fly Rail Baggage program, which allows you to check in luggage at your hometown airport (Denver, Duluth, wherever) and have it sent straight to the train station in Zermatt-much easier than lugging gear from station to station. Find train timetables at rail.ch.
To see Spiez on your way to Zermatt, you'll need to land in Zurich in the morning. Arrive in Zurich by 1:00 p.m., and you'll make the Matterhorn by dinner. The Glacier Express-glass viewing cars and all-leaves Zermatt at 10:10 a.m. If you don't want to sacrifice the ski day, faster, less scenic trains head to Andermatt in the late afternoon.
Detours: Spend a few hours in the town of Spiez, one of the stops between Zurich and Zermatt, and you can see 13th-century graffiti on a 12th-century castle plus a strange garden of hemp plants along Lake Thun. Boat cruises (bls.ch) are free with your Flexi Pass. On your way to or from Engelberg, check out the lakeside settlement of Luzern (luzern.org), which has a magnificent old town. In Zurich, get free chocolate on a tour of the Lindt & Sprüngli factory.
Safety: Dial 1414 to reach Switzerland's helicopter rescue service, Rega. Annual rescue insurance is also available at Rega's website ($25; rega.ch) and at post offices countrywide. Switzerland's version of 911 is 144. The Web site of Switzerland's Institute for Snow and Avalanche Research (slf.ch) has avalanche bulletins covering every region-plus color snow-accumulation maps for storm chasers.