The deaf problem occurs in splash overos that have pie bald markings on the head.
There is a very well known QH breeder who also had a line of paint horses. Many of his paint horses were deaf.
I was around a paint horse that came directly from this breeder. This horse was a stallion, stone deaf, and sired a large number of deaf foals. All of the markings were identical. They also have an ear set that kind of tells that they are deaf.
This stallion was gelded by his new owner. I think that he made up for his lack of hearing by being extremely aware of everything around him. The owner showed him in pleasure, horsemanship and showmanship at breed shows. He would catch something out of the corner of his eye and go ballistic. It really did make it hard for her to show him since he was pretty erratic in his behavior.
One of his sons, also deaf, was shown to an APHA youth championship. He seemed to have ringing, or something, in his ears. Sometimes he would shake and shake his head.
IMHO you have to have tons of patience and completly change your training methods to accomodate the lack of voice control.