I've played a lot of online horse games, and this is only the one I've been persuaded to spend RL money on because it's as realistic as it gets. Real life genetics and advancing all the time to reflect new discoveries in horse genetics!
Please check out Hunt and Jump, Inc. Or Hajinc! Our forum community is amazing, as I'm sure this one is from what I've seen. You can breed for ability, color, or both! The beauty of this game is that each person can play it their own way-there is no right or wrong. The complexity of it keeps me and hundreds of other RL horse lovers coming back year after year. And you can try it out for free!
Give Haj a try! I'm sure you will love it as much as I do!
HuntAndJump.com: Free Horse Genetics Game