It's not if you're r/l-handed, it's r/l-leg dominance which makes the difference. Most people would kick a ball with their right leg, but some with their left, same as most people write with their right hand but some with their left. Snowboarding, skating and surfing cater to this imbalance, but skiing does not which is why most beginners go through a phase of being better at one turn than the other. This imbalance comes back when you start freestyle skiing in terms of preference of direction. Since most people are right leg dominant, they prefer to spin left so they can set the spin from their right leg, and they prefer to slide stuff right foot forward so they can keep their weight on the front foot plus they've already learned to spin left so they prefer to do so onto a box/rail. However, as with some people who skate mongo or push with their wrong leg, some people spin in the opposite direction to the way predicted by this theory. At the end of the day it's down to the individual and how they get their head around it first, and once they have established their preference it can be very deeply engrained. This is one of the things which generates diversity in skiers/riders. One of my housemates even prefers to spin left so much that when he learned fs/bs270s out he learned right foot forward blind 70 before left, and left foot forward front 270 before right. His "natural" slide on rails depended entirely on what he did off it rather than which way he faced when he was on it.
