Replying to Cheap Skiing + Lodging

Hey everyone, I'm visiting Amsterdam with my family for a week (Dec 23 - Jan 1) and I figured that I would try do some skiing in Austria or Italy while I was in Europe. The problem is…I don't have much disposable income. I'm trying to plan out a trip but I have no knowledge of the region. I guess what I am asking is…where are the cheapest places to for skiing and lodging? I won't have a car while I am there either.

Another question that I have…what would be the best way to transport myself from Amsterdam to the mountains?

Any help would be appreciated, thanks a lot!