They have lots of versions…like Dreamer or Show Time or.. some other things!
References :

Riding Star. There are some different versions of this, and she has Champion Dreams First to Ride: Very focused on jumping. She’s played it so much I can hear the music in my sleep! This is definitely a great jumping game for her age.

Horse Farm — which is a broader game more focused on building stables, having foals etc. If you do get this one, look at her site below for the "cheat." I don’t like that term, but it’s the only way to play that game without getting totally frustrated.

Saddle Club is also an interesting game but tricky. It’s a simulation where you mount your horse then go all over the island looking for clues to solve a mystery. It’s pretty challenging and might be more fun for her in a year or two, though she did spent a fair amount of time on it when she got it about a year ago.
References :
horsecrazygirls.com