Kitzbuhel or Zell am See in Austria would be good for this kind of break.
One major problem though is that in Austria you will find it extremely difficult to get accomodation for less than a week during peak season. The majority of hotels only take bookings for Saturday to Saturday at that time of year.
Can't speak for other Alpine countries as Austria is the only one I'm familiar with.

I've just got back from Lapland (northern Finland) and there's lots of snow there. It was around 12-18 inches deep but up to 3ft in places!!!! Levi would be a nice place to go (we stayed in Yllas); they have a good ski and snowboarding area and a toboganing area called Kids Land, you'll be surprised how many parents enjoyed it more than the kids!! The ski-dooing through the pine forrest is excellent as well as driving a Huskey sleigh so lots of things to do which might not be available in other areas for a non-skier. I just loved driving down the artic roads in the hire car! It is a little pricey though.

Darren