A: You train for skiing with lots of squats. You train for snowboarding by bugging your Mom for more SoBe. (Does joking about snowboarders make me sound old? Because I am.)
Anyways, the key difference between the two sports is the lateral (side-to-side) shifting on skis and the sagittal (front-to-back) shifting on snowboards. Both require a strong core and quad-hip complex, so squatting and lunging reps will help for either sport.
Holding a boat pose will also help build hip control: For this, sit upright on the floor, lift your legs, extend your arms forward, and lean back to let your body form a V, all while keeping your lower back rigid. Calf presses will help build your forward-leaning strength.
Also, don't forget plyometrics. Paste a tape line on a carpeted floor, stand with your toes facing it, and, using both legs, do forward and back hops, five to a set, three sets. You can also train for snowboarding standing on Bongo and other balance boards.