The best way to train for skiing is to ski, but snow isn’t always available. You ski by bouncing up and down on your knees and shushing forward from your hips, so the best sports to prepare for skiing stress primarily your thigh and upper leg muscles: skiing, skating and cycling.
Running strengthens your heart and lungs, but it doesn’t make your upper leg muscles very strong because you run primarily with your lower leg shin and calf muscles. When you run, you land on your heel and use your lower leg muscles to help control the force of your footstrike and also to raise you up on your toes before you step off to the other foot. Running stresses your upper leg muscles only when you use them to lift you up when you run hard up hills.
You can develop very strong upper leg muscles by roller skiing, using a ski machine, roller skating, roller blading or cycling. Pedaling a bicycle stresses mainly your upper leg muscles, so the average bicycle rider is far better prepared for skiing than the average runner.