Mission Équitation: à la recherche du cheval d'or

Summary
You play as Manon (Lisa, US) who is apparently super gifted with horses. You encounter a special Akhal-Teke horse (Lingo) that is taken away from his owner, so you go all around the world to help people and to find Lingo.

Game Design
3D graphics. All horses have the same model, only their coat colours change. Some unique mechanics for special moves and even misbehaving horses. Seems to pride itself on it's "realistic" riding features, but also has horses standing around fully saddled in open stalls. Open world. No horse care.

Gameplay
You walk around and get quests from various persons.

Riding Mechanics
Mouse based. Scroll mouse wheel to change gait. Special moves require following a circle/pattern with the mouse or clicking/holding in the right spot. Special "interactions" also require following a circle with the mouse to regain control of your horse, like when they get spooked by something, or when they get distracted by food while you ride them.

Differences between Releases
The Nintendo DS release--