I've seen this twice now, once with my brother in a packed theatre, the second time in 3D on my own in a near empty room. Oddly I felt a little underwhelmed right after both times but then felt more excited the more I thought and read about the film.
I think that's to the credit of the film, too - it becomes this mirror for the audience, allowing many different people to identify with Elsa's conflicts - internal and external.
It's most obviously a metaphor for mental illness itself (Co-Director Jennifer Lee answered a tweet saying it was meant to show anxiety and depression*) but yes, a lot of the appeal of Elsa is that most everyone can relate to her in one way or another. Gender Identity, adolescence, religious persecution, etc. I even saw someone list dozens more examples on Tumblr but comically they then deliberately ignored sexuality.
The sad thing about 'Let it Go' though is that a lot of it isn't about accepting her powers but locking herself back up in a new room, emphasized when she closes the ice palace doors at the end of the song.
* Jennifer Lee
has actually answered quite a few tweets about Frozen, worth checking out.