Both sets of muscles of opposing muscle groups must be trained, along with the upper back. A regimine of sit ups can strenghten the lower back.
To train and strengthen the upper body for skiing at a work out facility, to begin with, I would suggest some lat pull downs, bicep curls, and some tricep extensions.
If at home, push ups from a knealing position [ this protects your lower and vulerable back. ] Tricep training by sitting at the bottom of stairs, your butt right next to the bottom step, with your palms behind you on the first step, and then lift your body SLOWLY and deliberately off the ground. Biceps, use some heavy cans of food as weights. Do two to three sets with about ten to 12 reps per set.
Elastic cords are also good.
Some other ideas: after skiing, stretch all your muscles, vigorously walk around including swinging your arms for about five minutes, pop about 1000 mg. of vitimin C and E each,take on some serious protein as soon as possible, carbo load for your evening and morning meals, avoid the booze with the possible exception of ONE glass of a flavanoid laiden red wine to be consumed with the protein, take on lots and lots of fluids, and get a good night's sleep.