Could try and get a couple of the teachers who are going on the trip, (preferably ones who like you), to convince your parents.
Get your brother on-side too, if that's possible; as if he makes clear that he thinks you SHOULD go, your parents may be forced to reconsider - after all, what parent would send an "unwilling" child over one who desperately wants to go?
Your parents perhaps sound overly cautious- if you fall when skiing, you fall, and so long as you are prepared to take that risk, what you put your body through should, ideally, be mainly up to you.
If in doubt, manipulate, manipulate, manipulate... A generally meloncholy appearance, interrupted only by tearful whimpers, etc. (Not too much though, you don't wanna be stuck on meds for depression, too...)