They really do look alike! Though seeing the movie horse's face up close - lol the star is so perfect with such clear edges it's easy to see that they painted it on his face for the film. I know that multiple equine actors usually share a role - one horse does a the close ups, one or more horses do certain tricks (rearing, nudging the human actor, laying down, etc), and usually one horse for running/far away shots - so they end up painting the horses to make the markings match.
Your old guy is adorable, though.