They don't get used to being sunburned on white faces/noses. They can however get skin cancer and do frequently.
Keeping horse up is best, at least during most overhead part of sun during the day.
Another danger of the sun is photosensitivity, which is what I am having to deal with in Kola's care. Got damaged last year due to something he was eating in pasture, (aslike clover possibly) but it reacted with sun and by time really got good look at him, liver damaged and hair getting brittle.
He is fine now, but will always have to be kept off of pasture, and up when sun is out and grass is growing.
Horses make me a better person.