Date rape, to me, is using physical force, drugging someone, etc.
But convincing them of the potential of a shared evening seems perfectly legitimate. As long as the person has the ability to walk out the door, it’s a choice. An adult choice, but a legitimate choice.
The song was written by a man to be sung every year by him and his wife at Christmas parties. They apparently were a big hit, and the wife was not happy when he sold the song.
Also, in the original movie it appeared in, two sets of couples were singing it, and the male and female reversed the roles in the second. I.E. in one version, the man was trying to convince the woman to stay in one couple's version. And in the other, the woman is trying to convince the man to stay.
Baby it's cold outside [From the movie Neptune's Daughter. Probably mostly remembered for this song - which went on win the Academy Award for best song.]