Imagine Champion Rider

Imagine: Champion Rider (or Petz: Horse Club in the US) is a game for the Wii, DS and Windows, the latter which can also come with Pippa Funnell: Ranch Rescue. The goal of the game is to save the mustangs on a reserve, and to win the Legend's Cup.

Story
You play as a teenager named Lily, who does horse-riding competitions. She occasionally goes to a reserve which is full of horses, especially mustangs. The reserve try to breed from them, but there is an avalanche and some of their horses go missing. You hear that a foal named Oscar is hurt and you go to help, finding out that you can do horse whispering.

Gameplay
During the game, there are lots of "missions", many of which require you to "Approach" a horse and gain their trust. Most of the horses (but not foals) in the game can be ridden, and you can even breed your own horses and make foals, which grow into adults as you care for them.