@musicmatters, you are making snappy, rhythmic turns, looking ahead, controlling your line. On this snow, on this terrain, your turns are working. Skiing is a sensation sport. We ski for the sensations, and it looks like you are enjoying the activity of making these turns. But, on more challenging terrain and on hard snow you may find your current movement pattern doesn't work as well.
What do you avoid skiing now in terms of snow conditions, pitch, groomed/non-groomed, trees, bumps? With a change in your fundamental approach to making turns, you could venture into new territory on the mountain and broaden the types of snow you enjoy skiing. Replacing your current movement patterns involves learning some new fundamentals and putting them in control, and suppressing what you do now. This change will be most successful if you find an instructor with whom you work well and take a series of lessons over a season.
At this point your turns depend on a lot of upper body activity. Your arms get a good workout as you swing them high and low to establish your rhythm. Your torso leans left for left turns and right for right turns, which helps edge your skis. Your shoulders rotate left to get everything below them started turning left, including the skis. Same for right turns -- the shoulders lead the turn. Your legs are doing some work, too, to help those turns work, but not nearly as much as they could. The legs follow along with what happens up above, while your feet and ankles simply go along for the ride.
Ideally, your upper body, arms included, should step away from the controls and let the legs and feet take over. With feet and legs motoring your turns beneath a "quiet" upper body, you could create the same rhythm you now have, the same short radius turns, and ski the same line, with less mass moving around above the skis and do it not only on this terrain but eventually on steeps, ice, bumps, and trees. The stable upper body would no longer threaten to throw you around and make you miss your turns -- on terrain where a missed turn matters. The skiing sensations will be just as rich and enjoyable, but produced by more subtle means. Take lessons, as this change requires someone watching you to tell you when you're successfully replacing the old habits. You won't be able to tell by yourself, as the current movements happen by habit, without conscious control.
By the way,
@musicmatters, what instrument do you play?
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Here are some stills from your video that show...
...the arm swings, which are more dramatic on the left side:
...the shoulder rotation:
...and the whole body lean:
Have a friend who used to plant the exact same way. Well it didn't stop him from skiing in some pretty nice places 
