As I am a (mountain) climber myself, I can reply with some knowledge:

I take my Minolta Dynax 505si (Maxxum in the USA) along in my backpack. It is very light and also the 100-300 weights nothing.
Be sure to have a fresh battery loaded.
A polarizing filter is good to have up there.

As for film, I always shoot Fuji color slides @ 100asa, but also carry some 50asa (forgot about the brand) in case the weather is perfect: blue sky, sun reflecting on the snow...