If people would pay closer attention to this very thing? Many horses would not be so sore.
I've never seen a horse that didn't have a shorter leg on one or the other side. Sometimes not by much, but can be substantial too.
Trimming the hooves to compensate for this helps, leaving the one that is on the short leg slightly longer for instance?
But when I worked with TB's, we flew vet in from Atlanta that was really good at this, and trimming should help.
For that matter? Humans, nor are any creatures, symmetrical on legs, arms, hands what have you. One side is always different.
Leather shims/pads under shoes is probably best, at least at first, but if farrier will trim correctly, should have this solved.
Horses make me a better person.