I have a horse with an eye cancer.
He has one brown eye and one blue eye... it's the brown eye that's the problem!
This horse may or may not be more prone to sun problems. Mine isn't, but some are.
In that case, put a mask on him only during the day time. At night, he won't be able to see well. If it rains, take it off - he can't see through the water well. Remove it and check his eyes at least once a day - if they rub the mask or another horse, they may get a dent that irritates their eyes. Make sure it fits well.
Tattooing eye liner does not protect against the sun. The melanin in skin is dark and protects, but just adding dye doesn't. In fact, it may make the skin MORE sensitive to light, especially the first year.
Many, many horses have white around their eyes, and very few have any problems at all. I'd make the trade if that's the only issue!
Edit: Buckinfun, white reflects far more light than dark. While the tattoo may reduce glare into the eye just as black grease put under a football player's eyes does, that's the ONLY benefit. Dye does not protect from the sun. The dark particles absorb more of the energy thn the light skin, and cause more problems.
If you've ever gotten a tattoo, you know they must be protected from the sun more than regular skin.
Far better to use some athletic blacking than to tattoo.
Edit2: Just read the article... says basically what I just said, and the opinion of a nurse specializing in cosmetic problems of humans is not exactly definitive.