You can best go to towns at high elevations such as Zermatt and St. Moritz, or the small villages of Riederalp and Bettmeralp. Whether there will be snow in town depends on the weather at that time, but snow will at least be close-by, one cable car ride away. Snowfall depends on the weather of the day, that can't be predicted. If you stay elsewhere in Switzerland there are plenty of peaks to visit to experience snow in March, e.g. Titlis, Corvatsch, Jungfraujoch.
Planning your trip is much easier with a free MySwissAlps account. Learn all about Switzerland and get in touch with us quickly if you have questions.
Let Swiss travel consultants create a customized itinerary. They will book your entire trip.