Story search: "Laughing All the Way" to Nuclear War

[Extollager]

TV or radio stations used to finish sometimes on Christmas Eve with a tongue-in-cheek announcement that radar had picked up an object moving from the North Pole, of a sleigh shape, etc. In this story, that touches off a nuclear attack.

Can anyone identify the story? I suppose it might have been a teleplay, but probably not. I have already checked Contento and done a simple online search without success.