How do horses train its young?

Through demonstration and disipline.

Part of what a foal learns, it learns from watching other horses, and copying them.

The other part is the other horses will disipline the foal when it does wrong. Say it gets to playig a little too roughly with one of the older mares. They may threaten to kick or nip at the foal. If a foal is really disobedient, the lead mare wil chase him away from the herd and put him in "time out". Keeping him away from the herd is scary for a horse, because within the herd lies saftey, and away from it lies danger. The lead mare will keep the horse away until he shows signs of submission, lowering his head, licking his lips, etc. then the mare would turn her back on him and let him go back the herd.