Do horses go grey with age?

Grey horses do - but often at a young age. Age-related greying similar to human greying does occur in horses, but not every horse. It's much the same as dogs going grey - they get grizzled around the muzzle and temples.

You can see some grizzling on the side of this guy's face. I also knew a horse that made it to 35 and never greyed at all, so it's highly variable.