Studies have been done comparing snowboarding and skier injuries. They occur almost at the same rate, but, as mentioned, beginner snowboarders seem to have a higher rate, with wrists the most common injury. As the rider gets better and goes for faster and higher in the air, shoulders, neck and ACL tears become more common.
Skiers injure their thumbs the most, but knee injuries are also common.
I believe that in either sport, if you are pushing yourself to progress, injuries will happen. It's still better than doing it on a Wii.