I think Anna is being held captive by the Snow Queen, who is going to be a bit villainous. Maybe she removed Anna’s heart before freezing her. However, the Snow Queen kept Anna’s heart in a jar so that the freezing spell would preserve her, rather than kill her. That could be how Anna is still alive in the present day, her youth and beauty preserved and not ravaged by the passage of time. That could also be why the sound of Anna’s heartbeat was audible. While this sounds extreme and maybe even morbid, it would be in keeping with Cora and Regina, who both have a thing for collecting hearts.
All of this…BRILLIANT!!! I accept this headcannon!
"If you go as far as you can see...you will then see enough to go even further." - Finn Balor