Okay, yes, Anna doesn't actually sing the song in the movie, even though this video by boblester122 still pairs her with the tune. But hey, if you wanna play as Elsa the Snow Queen instead, that's definitely an option in this GTA IV mod:

The mods aren't don't let you build a kingdom of snow out in the wilderness, but hey, belting Let It Go while reigning terror on the city still looks pretty cathartic.