I lot can be said about this song. What does it mean not to feel "natural" as a woman? Are women unnatural without the man? If she only feels "like a natural woman," is that like the way Madonna felt "like a virgin." She wasn't a virgin, but she felt like one (for one reason or another).
So, it's already a puzzling song, subject to many interpretations. Okay: What does it mean to sing it in a fur coat?
And can you think of any other occasions when what the singer wore affected the meaning of the song? The first thing that crossed my mind was Marlene Dietrich singing "Give Me The Man" while dressed in a tuxedo. But I don't think that's a good answer.
ADDED: "Her mouth was as wise as her eyes … and her voice was like her coat, rich and supple, and somehow full of secrets," wrote Patricia Highsmith in "The Price of Salt," which is now a big Oscar-begging movie called "Carol." The coat, a fur coat, looms large, as the costume designer Sandy Powell explained. It was "probably the most important item to get right."
"It’s those descriptions that don’t say what colour or shape it is or anything like a clue.” To interpret that impression of sexy, conspiratorial opulence, she says, she knew it had to be a blond mink, not brown, and not light or flashy.Fur is big now and deeply meaningful.