This great tutorial by the redstone master SethBling teaches you the basics of what we know as horse breeding. If you haven’t already, make sure you subscribe to him here: http://www.youtube.com/user/sethbling.
Here are three cool things I learned from this:
1. There is almost a 0% percent chance of taming a horse or donkey on the first try.
2. If you feed a horse before you tame it OR tame it with an empty hand, you have a higher chance of taming it.
3. You can mix and match breeding horses to get the fastest, highest jumping, and strongest horse possible.