I'm glad others have already recommended helmets and wrist guards. I fractured my wrist, well, technically my distal radius (arm bone near the wrist) snowboarding last Feb. I actually put my hands down behind me instead of in front. This happened on my third day out snowboarding, the first two times I borrowed my friends wrist guards, but I didn't have them this third time, and I can't help but think if I'd had them I wouldn't have had to be in a cast, go through PT, endure the humiliation of explaining what happened, blah blah blah. (I'm still undecided about trying again, something about being on a steep snowy hill going fast terrifies me. Put me on a steep paved hill on a bike going fast and I'm in heaven).
The other thing I recommed is knee pads, the volleyball type available at any sporting goods store. In addition to falling on your butt, you'll also fall on your knees which can get painful after several times.
A huge part of snowboarding is balance, and if you're good at balancing on your bike, you'll probably be good at balancing on a board. Have fun!
