I am the moderator on an online sim horse game called Horse Eden Eventing. Been there for a couple of years. The owner and I were friends before this game and I was lucky enough to be in Beta testing. This game has shot up in the ratings and is insanely cool. You basically can capture wild horses of certain eventing breeds and then you can breed them, train, show, horse racing, have riders, tack, trail rides, clinics, etc. And the breeding is based on real life genetics and I have actually learned all about genetics from this game! Haha Here is the game if you want to try it out.
Horse Eden Eventing
For every person that joins using the above link, I will send you a free horse too! Come join us, it's awesome!