Actually, that is NOT a blue ring around his eye.
The brown part of your horse's eye is the iris, which is the colored part of the eye just like in humans. The center black dot is the pupil where light enters the eye and your horse can "see".
Beyond the iris is the white sclera that you do see in humans, but you don't really see in horses. Horses have a sclera too but their anatomy has most of it covered.
So this blue illusion that you are seeing is where the brown iris transitions into the white sclera, which I will agree does appear blue in color. Underneath the sclera is what is called the choroid which is dark in color. So if the sclera ever gets thin, the dark choroid may show through with a blue-ish color (also see in humans) but again, we don't really see it in horses because their iris takes up most of the eye that we can see from the outside.
So it's not really a blue ring; it is just the iris turning into white sclera.
You can check out this website if you want more information on the anatomy. The Equine Eye
Except they do not have the choroid or sclera labeled in the picture.
This is a human eye, but horse eyes are actually pretty similar when it comes to the anatomy.