It’s not really that cold outside
I've just realised that "Baby, it's cold outside" is a rephrased song about leaving the swing party with a bad leader-follower ratio. The female vocal is, in fact, a leader who wants to go home after having danced for 3 hours straight. The male vocal is a follower who, after almost not having danced at all, finally gets a hold of her favourite leader on his way out.