We've played a number of different classical-music-style Christmas medleys in the Madison Community Orchestra over the years, and this one is clearly the best.
One reason is that it really isn't a medley at all. People who have tried to present it as a sing-along -- distributing lyrics to the audience -- have found that some of the keys that composer Leroy Anderson uses make part of it impossible for most people to sing.
It really is a symphonic movement, with the familiar tunes treated at times as orchestral "motives." It begins with one phrase -- half a bar long -- from "Joy to the World" and then rushes into "Deck the Halls," shifting back to "Joy" in the seventh measure.
The last section is a majestic version of "Adeste Fidelis" accompanied by a rhythmic phrase derived from "Jingle Bells." Amazingly -- it works! The coda is a rollicking jumble based on the opening phrases of “Jingle Bells,” interrupted briefly by “Joy to the World,” and a few measures that seem to derive from “Hark the Herald,” ending by hammering away fortissimo at the first two notes of the chorus of “Jingle Bells.”
Try doing that as an audience sing-along. But, boy, is it fun to play!