Go for the compound lifts. The big 3....squats, deadlifts, and bench. Compound lifts don't just work the targeted area. They work nearly the entire body for stabilization and power throughout the movement. Compound exercises also release the most growth hormone and testosterone of any lift, which will help improve your strength and muscle gains. If you do squats and deadlifts properly it'll work your core harder than any crunch or sit up session you can think of. These are the ones that you can not leave out of a routine. But just remember the most important part......proper form. If you don't use proper form you can seriously or permanently injure yourself. Start light while focusing on perfecting your form, than start slowly working your way up.
Bent over rows, military presses, straight legged deadlifts, weighted pull ups are also very effective and I wouldn't leave them out. Also don't do all of this in one day, it won't work well. If you are giving it your all and doing it properly, you shouldn't be able to do squats and deadlifts on the same day. Split the workouts. One day is leg day, one is back, the other chest (mixing in say shoulder/tricep on chest day and little things to each day to fit in). And try to separate leg and back day by atleast 2-3 days between them so as to properly recover enough to put your strength into them.
But another extremely important aspect of any lifting routine is the nutrition. If you don't eat properly 30-1hr before your lift, your lifts will suffer and you will fatigue really easily. Also after a lift routine eat about 1 hr after you are done so as to replenish nutrients that you used during the workout. (good post workout protein shakes are also a good idea for right after your done to quickly get the protein and other nutrients to your muscles). It's best to have proper nutrition through the whole day, but hey that might be asking too much. So focus on really eating right before and after the workout. Massive complex carbs and protein being the most important before and after workouts. Lifting really depletes your glycogen stores (so stock up and replenish with good complex carbs.
Don't forget to also warm up before you do any lifting routine. And research proper stretching techniques as it will reduce injury both on and off the ski hill.