As long ago as the 1950s I remember a very big Flat racehorse who used to run perfectly well, and win, who was one-eyed (this was in Africa, not in the UK), and there are at least three one-eyed horses running over jumps here at present, with no problems at all. Since the judgment on how to jump is made well before take-off, and no horse actually sees a jump as he goes over it, one-eyedness isn't a factor in determining jumping accuracy.
Incidentally, thinking of DEAF horses, I'm reading Muriel Lennox's book on NORTHERN DANCER, and it details the examination of HYPERION's skeleton. A large overgrowth of bone was found behind one of his ears, which indicated deafness or, at the least, severely impaired hearing in that ear. The explanation for his calm, dreamy life off-track then looked to be that, in the yard and in his fields, he couldn't hear very much, which also explained why he would run right up to birds and other animals to 'examine' them - presumably he wondered why they didn't make any noise. Then, due to the roaring of the crowds and the general noise on racecourses, his poor ear could at last pick up extreme sounds, whereupon he became animated, picked up his performance to brilliant effect.
Incidentally, thinking of DEAF horses, I'm reading Muriel Lennox's book on NORTHERN DANCER, and it details the examination of HYPERION's skeleton. A large overgrowth of bone was found behind one of his ears, which indicated deafness or, at the least, severely impaired hearing in that ear. The explanation for his calm, dreamy life off-track then looked to be that, in the yard and in his fields, he couldn't hear very much, which also explained why he would run right up to birds and other animals to 'examine' them - presumably he wondered why they didn't make any noise. Then, due to the roaring of the crowds and the general noise on racecourses, his poor ear could at last pick up extreme sounds, whereupon he became animated, picked up his performance to brilliant effect.