I recommend you bring me and my snowboard, Mavis.
As far as a housing, you could maybe just get away with bagging the camera with a rain sleeve of some sort. With only a couple of days, you might just want to pack a garbage bag or something and improvise if needed.
I don’t know enough to give advice on the polarizer other than that I think they’re quite directional (I use CP filters on my still camera frequently). That could present problems unless you can change the sun’s position relative to the earth. Also, on wide shots I’ve experienced shifts in the sky.
Cf