That’s the amount of difference that the explicitness of the WAP lyrics makes to me.
WAP is about an independent woman getting what she wants; in Baby It’s Cold Outside the woman sounds scared, confused, reluctant, and jerked around by the pressure applied by the man and the drinks he’s loading her up with and by the neighbors and broader society, and even the forces of Mother Nature.
She has no agency and we’re supposed to think it’s sweet and cute, I guess. No thanks.