Squats, with squats and some squats to finish it off. I also recommend some ab routines, P90X's Ab Ripper X is a really good no-equipment circuit.
All that said, I recommend cardio and good nutrition as well, it helps a ton with keeping stamina up/feeling better over all. Swimming would be ideal cardio as it works your upper body a ton more than running or bicycling and is much lower impact on your knees/joints.
Pretty much this. I only really do compound movement exercises anymore.
Squats, deadlifts, bench press, pull ups, dips, shoulder military presses and core ab work will make you rock solid for the ski season with functional muscle strength and the padding necessary to withstand some gnarly falls.
Run hills if you can to give your legs the muscular endurance to ski multiple days in a row.
Bike for 15-20 minutes, bench, dips, tris, lat pull down, leg press, clean, dead lift, upward row, sit-ups, inverted, and roll out. Every other day and stil I am overweight fml
I work out pretty much all year round but find cardio and core strength help me most for skiing.
I do HIIT training to give my cardio a boost before a ski season. Everything is harder in the mountain if you're not used to the altitude so getting your body efficient at working max out with less oxygen helps. I do stair running, hill sprints, sprints on the rower and cycling.
For all round strength I go with push ups, pull ups, dips a core routine and squats. I don't really need to train legs too hard but if your legs are weak then training them will certainly help before you ski.
I'd say various types of yoga for balance, strengthening and recovery as well as core exercises. You don't need to go spend $20 on a yoga class to understanding the stretches and poses either, just look up videos online, etc. Lifting and cardio will also allow you to maintain upper body and leg strength which are important to protect your joints (shoulder/hip/knee) when you fall. However, even if you have strong muscles surrounding say your shoulder joint, the force of a high impact fall won't always save you, but it can prevent injury on more minor falls. And as most people mentioned above, the more you ski the stronger those specific leg muscles will get.