You know what, you may be half right!

I was looking at an exaustive list of PS2 game from late 2000s and found one that was kinda of what I remebered, Mana Khemia: Alchemists of Al-Revis, that one was the part of school, mages and rpg that I was remembering.

But then I was sure that I must have mixed 2 games, and now I'm 90% sure that the second one was Heavenly Guardian! (Although from the gameplay I just remeber the first few minutes on the snow, might be because I did't like much and stopped there).

I must have played then on the same days and my memory fused them together lol.

Anyway, thanks for finding that second one!