In reply to Rick Ashton:
For wrists:
Towel pull ups have been mentioned already, which would be a good sport specific exercise.
Plank, side plank on a straight arm.
Reverse curls or Zottman curls
Inclined ring rows with your thumb upwards like holding an ice axe
Push ups on your knuckles
Push ups on parallel bars
I would also recommend using the elbow tendonitis weighted pronation and supination exercises but use heavy weights and stick with 6-8 reps, 4-6 sets.
For shoulders I would recommend ring flies and scapula abduction.
I would also suggest you try dish and arched body holds for core, so you can keep a high axe pressed into a marginal placement high above or behind you if on steep ice.