Do horses, like humans, have a dominant side?
Absolutely. Horses have the same "handedness" as humans - which we observe in training as them taking longer to learn to turn properly to one side over the other and preferring to canter on a certain lead.
And, just like in humans, the right side is more often dominant - which means the horse is stronger when moving to the left.
So, yes, horses are handed - and most often right handed, just like us. (Sorry to the southpaws reading this).