You can zoom with the Canon S3 and it has optical image stabilization.
Most digital cameras that zoom during movies will be limited to 'digital' zoom rather than what you want which is 'optical' zoom. Digital zoom simply crops to lower resolution as you zoom. Optical zoom is the normal zoom in closer while maintaining full resolution.
http://www.dpreview.com/reviews/canons3is/
With 4gig cards on sale at places like Radio Shack for 27 dollars, there is not much reason to mess with tape anymore.
It's also got a great 12 to 1 zoom and an optical viewfinder. The electronic 'look on the back of the camera' viewfinders can be hard to use in bright sunlight.
I've used the S2 for a long time with nice results. The S3 is the newer version of the same camera.
If you are thinking about a different point and shoot for ski movies, just make sure you can take it back if you find out after the fact that you can't optically zoom during shooting. Almost none of them do. (despite what an ignorant sales person might say)
btw - Hi Everyone. I'm off to do Marathon 19 in Huntsville Alabama then Marathon 20 in Jacksonville FL the following weekend. (since Feb 07)
Then I'll be cutting back to do some skiing. Maybe the mystery poster HH was quoting recently about the new Head Boots and some others (Hobbit - you around) would be interested in a 3 dayer just ahead of Christmas.
Maybe I could use a "Raptor" like Christmas present