Your headcanons of an MCU x Frozen AU where Anna is part of the Avengers Initiative because she was found by Fury, thawed, and is the Ice Woman of the Avengers due some ice that remained in her heart allowing her to have some Ice Man powers
Original thought!
Just like Steve, she wakes up in our modern world in a decoy studio that is made to accustom her slowly but she escaped, discovering the energetic world around her. The iconic line "I had a date." stays the same, only she means Kristoff. She had planned a dance with Kristoff.
When she escapes, she accidentally uses the ice and snow powers she has (and developped in her wake? or during the thawing process? or maybe enhanced by SHIELD technology?) and it reminds her of Elsa, putting her in an overwhelmed state truly
Calls herself the Ice Woman when she is asked about her superhero name because she wants 'Snow Queen' to belong to Elsa forever
She catches up with pop culture pretty fast because she wants to be included in the Avengers team (she hates to be outcast, you know), and after watching The Incredibles, she has a serious reflexion on whether or not her supersuit should keep the cape lol
Plot twist: she eventually finds out that Elsa is alive; she had trapped her own self in ice when trying to search for her
THE EMOTIONS.
Send me a Frozen AU and I'll give you 5 headcanons! :D