What is the name of this anime movie?

All I can remember is that it start out in a snowy town and a girl meets a man. I know that the man is a painter and gives the girl a necklace. (not Howls moving castle) They meet years later and then split off again. She searches her life for him but he dies in jail, but she has no idea. So she keeps looking. At the end of the movie she goes to the moon and finds a painting on the moon.
That's all I can remember.