There is no need to traverse the overworld on two legs if you know how to breed horses in Minecraft. All you need are two tame horses and some Golden Carrots or Golden Apples.

Before you can start a horse family, you need to find some horses and tame them.

Find two horses. Horses graze in plains and savannas. Horses have no gender in Minecraft, so two will suffice.

Tame the horses. With nothing in your hand, interact with a horse to mount it. It will probably throw you off a few times, but keep trying until you see hearts floating above its head.