I believe all greys fade to white, it's just a matter of the horse living long enough to reach that point. Some horses grey faster than others, some horses very slowly grey out. A foal isn't born grey, but their coat can give you an indication if they will grey out or not. Usually, the foal coat is a more "mature" color(i.e. darker), the legs are usually darker, and sometimes there are "goggles" around the foal's eyes.
There on the tips of fair fresh flowers feedeth he; How joyous his neigh,
there in the midst of sacred pollen hidden, all hidden he; how joyous his neigh