Make sure you get lot's of sleep at night - but you know that from your cross fit. Besides hands - your groin and hammies are vulnerable. Due to the amount of skiing you will be doing make sure you don't get a fatigue injury - like flipping over the front of your ski when tired. Some lactose threshold training will be beneficial - working out at the 80-90% level of your max heart rate. Do this a few times a week thru hi intensity intervals. This will train your body to process and buffer lactic acid buildup.
If you're going to train hard at the school get a heart rate monitor, if you start working in your 90% and up range - not hard to do if your cross-fit training - you want to stay out of this range otherwise your fatigue and muscle pain will not cease between days.
Or you could blood dope
and where the best gloves you can afford