Gargoyle, I agree about Longfellow's song (poem) and its origins being "heart-tugging" and not really in dispute.   That's one for which the various attributions and histories seem quite consistent.

Q, Yes, you are helping, not adding to the confusion.   But what did add to the confusion was a Christmas music program on NPR tonight wherein the music for Joy to the World was, yet again, attributed to Handel!

mrdux, thanks for that citation too.    I'd disagree about the attribution to Handel resulting "solely" from the opening of Messiah resembling parts of JTTW.   Mason himself, when he published his tune, sort of credited or cited Handel, though it's thought that he may have just been acknowledging a GENERAL musical 'debt' to the earlier great composer.

BTW. as to the first notes of Joy to the World, as it happens, the first 8 notes are precisely a descending musical scale (octave) (with syncopation of sorts).