Way back in the olden days when I learned to ski in the winter of 1968, I dog-eared the iconic book "Learn to Ski" by Bob Beattie as a way of introducing myself to this wonderful sport. At the end of the book they had an exercise section which included the also iconic wall sit exercise as a means of improving your thigh strength. This is the one where you assume a seated position with your back up against a wall and hold it for as long as you can. At my best, I could do it for over a minute.
It's a good exercise as it conditions you to endure the lactic acid build-up in your quadriceps. And it does build strength.
And then there is that "Skier's Edge" thing that some people use. Also effective for building thigh strength, but not for helping your thighs rotate left and right.
So hold on a dang minute! I just intimated that there is another use of the quadriceps that helps build your skiing skills—and that's the rotary capability that your thighs can do. And it's a very highly important skill if you want to be an advanced skier.
Here's what I mean: stand up with equal weight on both feet and twist your thighs to the right. Not your knees, but your thighs. You'll feel your quads bulge in that direction. Your feet or knees probably won't turn to the right, but that's ok, they aren't supposed to.
But when you are in your skis on snow, and the resistance of the snow to the torque is less than that of your floor, that bulge enhances your turning ability. Think about steering with your thighs to the left and right while you ski. It's not easy, trust me. And it hurts just like that wall sit, trust me on that too.
When you get the hang of it, however, you will discover that this thigh twisting is an important means of keeping your ability to counter, or face down the hill. And it keeps you in balance. And it helps you maintain simultaneous skis. And it helps to keep your feet under your hips, all of which are essential characteristics of an advanced skier.
Try it. You'll be amazed.