You're horse didn't jump out, they can't jump on their own over fences. It despawned. It's a known bug in this new update that horses despawn even when hitched or saddled. Naming them with a nametag seems to be the only way to keep a horse. Also horses don't tame right away, they take a few tries of being ridden to be tamed. Use wheat, golden apples or golden carrots to help the taming process.
You need to tame the horse to ride it, and toy do this by repeatedly getting on (And getting kicked off) until the horse creates the heart particles. This may take several attempts, but the process can be sped up by feeding the horse suger, bread, apples, wheat, and haybales (You can also use these foods to quickly grow babies).
But horses still despawn, unless you name them with a nametag. So if you don't name them, be sure to remove all saddles and armor before you leave.