I am giving my educated guess that the "Ice Queen" is an ENTJ.
She strikes me as an extrovert. I read something about how she'd be the last to leave a party. As a teen she'd go out alone to gay clubs and that's how she got into the music scene & formed her glam look. I don't see too many introverts going out to clubs alone as a teen.
Her cold delivery seems Te. Plus, she is one of the rare female lyricists to very rarely write songs dealing with romantic relationships.
I see Ni in her lyrics. The symbolism seems constant (ie. the whole song "Cities in Dust" is clearly symbolic for something other than its literal telling of the destruction of Pompeii).
To cement her as a J, I've also heard she was very controlling in the band and ruled with an iron fist. Her style, although strange, is impeccable (contrasted to the smeared lipstick of INFP Robert Smith). Her look and stage persona (very dynamic performer) seems to show her tertiary Se.