This was triggered by finding a video on Youtube of somebody who was blind in one eye and could barely see out of the other jumping.
Blind people absolutely can and do ride horses. They even compete. Blind people routinely compete against sighted people in dressage - some have "living letters" but some do it by literally counting their horse's strides (even more of a challenge when you realize that if they change horses they have to learn to count all over again).
Blind show jumpers either have a sighted rider to follow or their trainer shouting instructions. Bells are sometimes used.
There are blind cowboys who ride broncs, both saddle and bareback. At least one barrel racer can literally see no further than two inches from her face.
So, by all means have your blind characters ride - and ride well. They just need a horse that can be trusted to be their eyes.