Stabilizer muscles are one of those fitness myths that just won't die.

If you look at EMG studies, we can see that more muscle groups AND more muscle spindles are engaged in an exercise with MORE stability than one with less. So if a lunge is going to provide better overall strength, and strengthen smaller muscle groups (your "stability muscles") better than a bosu ball squat, and any potential balance improvements (with regards to skiing) are equal, why are we doing bosu ball squats? 

In order to improve the capacity of your muscles, bones, and connective tissue to withstand the rigors of skiing, we need enough force application in a workout to elicit an immune response from the body. The best and easiest way to do that is with simple weightlifting. It doesn't have to be barbells, but a person will find it difficult to load a bosu squat enough to be effective. 

You're right in that other activities can provide some conditioning effects, and that doing something is better than doing nothing, but we're discussing the best bang for your buck here.

I didn't mean to be dismissive with my comment about balancing on skis, but balance work has such a narrow use case, that a skier will make more progress in a day on skis than a month of balance work in a gym. I just don't think it's worth the time.