It happens to nearly everyone; make sure to take suncream and that you put it on. The suns rays penetrate cloud much more than you expect and love bouncing of all that reflective snow to burn into your skin! It is also advisable to take a UV stick for your lips and to keep applying this.
Clearly a serious injury will put a major downer on your holiday. The best ways to avoid one are; wear protective equipment (I am a big advocate of wristguards), fall properly (you should be taught this in lessons) and don't try and exceed your limits too far.