I sang Rudolph the Red Nose Reindeer to the tune of Villulia (56b in the Sacred Harp), tune written by (or attributed to) by J.M. Day, 1850.

(MP3 of tune here.) Singing "Rudolph" to this tune was first reported to me as an event at a "Dirge Night" held by Norumbega Harmony in the Boston area, so that makes it an actual folk song collected in Massachusetts.

--Charlie Baum