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I read this series around 9 years ago and honestly, I don't remember a thing about the plot. At any rate, I remember enjoying it. I'm not even certain that it was a trilogy, but it was definitely a series and all the books were published before 2006 thereabouts.
So what I do remember is that the main character was a girl and she had this slightly older mentor (male, and his name might have started with a 'C'). I have no idea what they did or if they had a quest (they probably did though) but I do remember that at one point she was trapped in a place or castle in a very cold, snowy environment. In fact, I'm fairly certain that the cover of the second (?) book was a very wintry one of the girl in said cold environment.
I also remember that at the end of the series, she didn't end up getting romantically involved with her mentor even though young me was desperately rooting for them. I was rather upset about that. It was also one of those fantasy series with an appendix of sorts at the back expanding on the world and briefly expanding on the background of the guy, if I'm not wrong. The appendix also talked about the girl and her various names, like a prophecy name or something.
There might also have been a tree involved somewhere, but I might be mixing that up so don't take my word for it about the tree. Anyway, I know this is about as vague as it possibly gets, but I'm giving it a try anyway!