Man in hiding from killers, forced to kill the woman he is living with to further hide his identity

Killer in hiding in arctic weather, kills woman hiding him.


I have not seen this, maybe?:
“Polar” (2019)


Or maybe this one?:
“The American” (2010)

The movie starts with a professional assassin (George Clooney) with his woman/lover in a cabin in a snowy environment, then an other assassin appears and tries to kill Clooney’s assassin, and Clooney kills his lover.
Quote from the below Wikipedia page of the movie:
“Jack and his lover, Ingrid, are relaxing in Sweden. As they walk in the wilderness outside their cabin, Jack becomes alarmed by a trail of footprints in the snow and pulls Ingrid towards shelter. Sniper gunshots ring out. Ingrid sees Jack pull a gun from his pocket and shoot the sniper. With little hesitation, Jack also kills Ingrid before locating and killing another armed man.