A woman at the barn I board at has an appy mare with uveitis. She has two fly masks on at all times to further shield her bad eye. This past summer, it was flared up all summer, and needed two types of ointments applied twice a day. She had a dose of bute every morning to keep her comfortable. After months of fighting with it, the owner decided to get it removed and be done with it. The horse acted like it only had one eye its entire life, nothing changed pre and post eye removal. The only difference now is that the horse isn't in constant pain during flare ups.
This horse was in its late teens, and was already broke and very used to be around humans. If I had a young horse that had uveitis, I would focus on getting it as far as I could with two eyes, transition to one eye, and act like nothing ever happened. Horses are great at adjusting to having only one eye, and will figure it out quick.
In the case the other eye starts flaring, there are horses that exist with both eyes removed, most famously Endo. You can look him up on youtube and social media, his owner competes in working equitation and dressage, and he is VERY competitive, despite being blind.
Toofine - 1998 Half Arabian
Minnie - 2013 Morgan