As most of us know, Hair defines who we are.
Lady Gaga is saying that her hair interprets her mood, personality, and who she is in general and she believes that HAIR is a perfect symbolism of FREEDOM.

Wanting to 'wear her hair' however she wants without being judged and to be free to be herself.

Hair explains who she is and she doesn't want anyone taking away the one thing she has... which is hair...

SHE IS HER HAIR... which means... her hair represents who she is or how she is feeling... a GREAT metaphor! :)