You basically play through your school weeks at a RIDING ACADEMY, where you do get grades based on your ACTIVITIES which you get to plan yourself at the start of each day, if I recall. 4 Activities of your choice per day, I think. Some Activities affect your GRADES (you need a minimum grade average each week), some are SOCIAL ACTIVITIES (optional visual novel type conversations basically, but offer fun rewards, like access to player & horse COSMETICS), and you can also take yourself to the library to study up on horse care (in-game horse care that helps you play). Definitely a strategy game, like the tag says.
The Dressage, Cross Country Riding and Show Jumping activities all had their own minigames. They all had more or less to do with timing, and you'd need to play through each one (at least) twice per School Week to get a decent grade average and proceed to the next week.
I think I recall the game also had a Photo Mode. While exploring the map, you'd sometimes need to capture a photo of a specific item or object on the map. Finding the object in the big open map based on a clue/riddle/instruction, that sort of thing.
Every school Week would end with a sort of special freeroam sequence in the game world - definitely a highlight of the game because it offered variety & the soundtrack was great in the open world parts - be it sneaking around forbidden areas without being seen or generally snooping around and solving mysteries.
I've played this game through a few times on the PS2 console back in the day, and it's one of my favourite horse games of all time. And I've played a fair bit of horse games. I'd love to see it on GOG because it's a top tier horse game and I don't see too many of those these days. For the horse riding fans of tomorrow, this would be a lovely game to see remastered. It has gameplay variety, interesting characters, pretty decent mystery plot and a very good soundtrack.