This is a horse jumping and agility game I enjoy the controls of. I keep hoping they'll add a racing segment to the game.
http://apps.facebook.com/ridingclub/
The Petz Horse Club series is also good, and they have an interesting mouse gesture system for taming wild animals.
And of course chocobo racing from FF7 had a popular control scheme involving a stamina meter that could be used up faster for bursts of speed.
The main thing I wanted to comment on is that even though the player's animal gets stronger, you never want the player to win a racing game more than 70% of the time, so the opponents have to get stronger too. Ideally there will be at least one opponent animal that is slightly faster than the player's but worse at steering, which allows the player to travel the course more efficiently. One opponent could be the opposite too, slower than the player but travels the course with maximum efficiency.
TYVM for this, after playing the riding club I much prefer it's controls to what I was doing. I like how you press once to get the horse going rather than holding it down, then you can hold down the button to "canter/gallop" faster like a shift key to sprint. Then to turn/look I'll have it so you slide your finger anywhere on the screen to pivot that direction rather than having to touch the touchpad.
I haven't checked the swipes in the other game for taming but definitely will. Also thanks for clarifying the 70% threshold, I was just blindly guessing how it should be.
I'm torn on whether I should do a toddler mode or very easy and then a normal mode. In the toddler mode running up to a jump would automatically make the animal jump over, so all you have to do is steer and line up with the jump and run into it. Then in toddler mode it might just be several mini games rather than the open world. Like the stable you can view all the different animals and information about each, wander around the paddock, maybe go for a ride. Then in normal mode you have to press the jump key at the right time to clear the jump, and have the whole "rpg" aspect where you unlock new animals and travel around earning money, competing in races, etc. And in your stable would only be animals you've already tamed. Initially the game started as a toddler game and then I added riding, leveling, and other stuff that makes it too complicated for little kids.
Similarly I probably need to add an option for accelerometer to steer as an option as well.