I broke/sprained my wrist 2 seasons ago..never got it checked out for real so not sure which..but it still hurts 2 years later so I am going to guess it was the former. I bought a really low profile splint from my pharmacy, wore it under a glove. Couldn't grip a pole for abouth a month so just skied with one...then once I had grip kept the splint on and skied with both poles. Yeah, it hurts to fall on..just make sure you don't put your hands down though and you should be good.
Having said that..I am not a doctor. I don't know what was wrong with my wrist. Not sure if I did more damage to it that way or not. I just knew I didn't want to go to the doctor and I wanted to keep skiing.