We have a good friend with a horse who is informally giving BonnieBlue riding lessons. I don't know if I want her to learn how to jump, though (a little GWTW reference).
The horse's name is Tank and BB loves him!
So far this summer, she has learned to back him up, stop him, turn him, and post.
BB likes to brush/comb Tank before and after the ride. Wisely, she's a bit afraid of the front end, but we're trying to teach her that the rear end is more dangerous. Tank goes out of his way to NOT bite when being fed a carrot or apple (all lips, this one), but I'm afraid he's going to kick her if she's not careful about giving his back end a wide berth.
She's learning patience because Debbie has to ride first, then her little girl, and then BB. It's just a great all-around experience for her.