Both my dogs are right-sided. My mare is right-sided too.
But I think you have the effect on the canter backwards. Most horses are right sided and the muscles on that side are more developed and tend to contract, so the untrained horse tends to fall onto the left lead (and run out to the left, and be unable to change to the right lead in an emergency). Once the horse is properly schooled to be straight, and to strike off from the trailing hind leg instead of falling onto the leading leg, he will take the right lead.
Polo ponies, which by and large don't get a lot of advanced collection work, have to be cantered extensively to the right to make them keep that lead (most polo players are right handed and want the pony to keep the right lead so they can't be ridden off). I speak from experience here because I exercised a local polo player's ponies and asked him if he wanted collection drills. He said, "Nah, just canter 'em around to the right 10-12 times."
But I also have a learned authority -- Noel Jackson in his Effective Horsemanship has a whole chapter on 'sidedness' in horses and its consequences.
I even went and checked to make sure I didn't have it backwards. It's Chapter X - "The Horse Straight".