I normally bring my camera bag with all my stuff in it to the top of the park or wherever im filming, and then take out what I need and hide the bag in the woods or talk to the park crew to see if I can keep my stuff in their little building. I've also gotten away with asking the lifties to hold my stuff for me to keep it dry and safe, but only if I know and trust the guy.
I wouldn't be too worried about it getting it wet unless the conditions are super wet. The only thing I'd be worried about is falling on it and breaking it.
This is why I use an IPhone with a juice pack. Stable video (auto stabilization). Plus you can actually ski without having to worry about a camera because your camera is in your pocket.
camera and lans in gallon size ziploc bag when heading from outside in the cold (if under 30ish) so the sudden warm air from the lodge doesn't cause condensation inside your camera and lens and will instead condense on the bag.
Skiing with an SLR comes with a price: not being able to do shit. Personally I ski with a smaller but stil relatively good quality Canon Vixia camcorder and if someone or myself is throwing down then we film. If nothing woth filming is happening I ski with it in my pocket, no problem. If your skiing with an SLR be sure that every lap counts.