In reply to Bobling:
Was in Zermatt a month ago and there was plenty of snow then, so it's fair to assume there will still be plenty at the end of March.
The skiing was awesome, but yep, it's ridiculously expensive.
However if you're there you may as well enjoy it, so go skiing. If you are capable, the itineraies (marked, off-piste runs) are brilliant and you still get fresh tracks days after the last snowfall. The Gornegrat railway is covered on the lift pass, but I'm sure you can get simple return tickets for the non-skiiers and the views are amazing. I'd imagine non-skiers could also get to the Kliene Matterhorn - even more spectacular.
Fondue at the WhymperStube was very good