I heard that "Baby it's cold outside." was originally feminist in it's day, it's just that in modern times it's become much more creepy.
According to some random person on the internet, the song is not about a man forcing a woman to stay but rather a woman who wants to stay but needs to pretend she doesn't because sexual mores were fucked up back in the day. The line about "Say, what's in this drink?" is not about date-rape drugs but rather a standard line where a woman pretends a non-alcoholic drink has alcohol so she can excuse her actions as the result of being drunk.
Again, all of this according to some random person on the internet. Don't take my word for it.