I've ridden three horses that were missing one of their eyes.
Two were already seasoned mounts when they lost the sight on the one side. Very little difference for them. One wanted to crane her neck around and check things out more than the other. The gelding that I'm thinking of, just goes with whatever we ask.
The third, lost his eye to an accident as a late two-year old, before he had been backed. There was a difference in cuing to his blind side (right) as he learned to respond to neck reining. He was always a couple weeks behind with everything to that direction.
Working cattle is a bit funny with him. If the animal gets in his "blind" spot, he tends to think they are gone and you can tell he is not thinking about where the cow is. Then when they pop back into his field of vision, he used to startle, but now still seems a bit surprised. His owner is starting to rope on him. I think selling him to a lefty would be easier, but she'll get it done.