Ah voldemort, thanks for that. I think I understand what you mean.
I would say a piece of music is in Am if there were generally no sharps or flats in it (as in like playing in C) but the song kind of returns to Am as its home, and sounds like it is in a minor key. Not a very technical description, I know, but is that about right?
By the way, did we learn the same version of the frozen song? The Disney one I had a go at is basically in Fm, I think, with the chorus sounding more positive in A flat, and the bridge y bit in E flat.
I wish I knew more about music theory! I'd be a much better pianist if I did.
After I had figured out the basic chords to this song, and got the introduction what I thought was about right, I had a look at the sheet music as mentioned up thread. It's a bit daunting, looking at so many notes on the page, but I know enough to follow the shape of the introduction (this is only because I already know how it is supposed to sound!) I was playing the right notes in the right order, but was surprised that you are supposed to play fifths in the left hand - I was doing my usual lazy thing of just bass notes in the left hand and playing the top notes of those fifths with my thumb. Since then, I have been trying to play it correctly and it took my ages to retrain my brain... have played it about fifty times, ie every time I walk past the piano, and only just stopped hitting bum notes. It was so much easier for me to just think in terms of Fm, C# (I know, I know, but that's what I call it in my head regardless of what key I am playing in 
) E flat, B flat minor/then major next time.
There is a lot to be said for being able to read music, and I wish I could do it!!