[PS2][2000s] 3D Open-world game with a horse, giants, and a desert

Platform: PS2 Genre: Action-Adventure Est. Year of Release: 2000s Graphics/Art Style: 3D realism Notable Characters: I wouldn't know. You play as a man who has a horse, and there's giants you have to fight. Notable Gameplay Mechanics: Well, horse-riding. One big thing I remember is that you can bring the horse to a stream and have it drink water. The controls for getting on and off the horse are on the screen. Other: There's three big things I remember about this game: A desert with a large skeleton you ride under, a fight with a giant/golem who's submerged in the ground, and in that arena the horse is moved to stand upside down on the ceiling. I've watched a LP of Shadow of the Colossus, but I really don't think that's it...

(Sorry if this isn't formatted right. First time posting and also on mobile.)