Get a gopro!
I know it doesnt have zoom, or even a screen to see what your filming, but if you think about it, you dont really need that stuff for about 90% of filming you do while skiing. Stabilization is good because you stick it on the most stable part of your body (your head).. It's also only 300 bucks and it shoots 1080p video and comes with a huge wide angle standard.
I made this using mine the other day.. Just an example
Benny B Pick n' Shovel from Mike Smith on Vimeo.