when horses are on a left lead they're pushing on with the right hind.
Same applies for right handed humans in ice skating. Right handed people always feel more comfortable and have more power going in left hand circles.
And vice versa
As for figure skating, that's a pretty broad blanket statement to make. You can't possibly know that ALL people feel more comfortable. I am right handed, and I drive with my left hand. Me and my sister are both right handed, and we hold our knife/fork in opposite hands when cutting meat.
I understand what you're trying to say, and I'm sure it's true in a lot of people, but through the years I have come to see that preference over which direction you ride better in does not correlate to left or right handedness.
I'm not saying ALL stiffness problems are as a result of the riders preference, I'm just saying it can often by a mitigating factor especially if your HORSE has a preference to go the side you also do, making the "weak" side a challenge for both of you.