Check out the Oxford Book of Carols, which will explain that carols are sung all year around.

The slaughter of the Innocents story to me seems like an instance of folk process collapsing of different events into one story. Herod probably did something like this, sometime. It was retoractively grafted on to the story of Jesus so that he would appear to fulfill an OT prophecy. All genuine Biblical scholarship will tell you that this is how Jesus came to be believed to have been born in Bethlehem, for example. If he was born anywhere other than Galilee, where he was raised and he began his work, it was Jerusalem.