As far as the feet go, sometimes bigger feet = worse movement.
Your horse doesn't have small feet and for anyone who wants to know, smaller feet are just a trait of Quarter Horses in general.
Still, it's genetic which means that most horses hooves will fall into that 68% region where normal hoof size is located.
Most of the halter horses do have smaller feet, but what you see is specialized shoeing. They're really not that small. A lot of stallions are discredited for passing on navicular tendencies through poor hoof genes, so the breeders really don't want them all that small.