But even if it were already Christmas, is "merry" the right word to express the religious meaning? The American Heritage® Dictionary defines "merry" this way:
1. Full of high-spirited gaiety; jolly. 2. Marked by or offering fun and gaiety; festive: a merry evening. 3. Archaic Delightful; entertaining. 4. Brisk: a merry pace.
E. Cobham Brewer's Dictionary of Phrase and Fable (1898) traces the history of "merry":
The original meaning is not mirthful, but active, famous; hence gallant soldiers were called “merry men;” favourable weather, “merry weather;” brisk wind, “a merry gale;” London was “merry London;” England, “merry England;” Chaucer speaks of the “merry organ at the mass;” Jane Shore is called by Pennant the “merry concubine of Edward IV.” (Anglo-Saxon, mœra, illustrious, great, mighty, etc.). (See MERRY-MEN.)
’Tis merry in hall, when beards wag all (2 Henry IV., act V. 3). It is a sure sign of mirth when the beards of the guests shake with laughter.
"Merry" has little to do with the message of Christianity. It connotes eating, drinking, dancing, joking, laughing, and horsing around. "Merry" turns Christmas into a generic winter festival. To express the spiritual happiness of Christmas, you would do better to say "Joyous Christmas." But the word "joy," standing alone, contains the meaning of Christmas.
Why not make the one-word expression "Joy!" the seasonal greeting? It's both more inclusive and more Christian.
UPDATE: "Merry" is only used in four places in the English translations of the New Testament that I checked. It is used in a positive way to describe the celebration of the return of the Prodigal Son and in this short passage, but it is used negatively in Revelation and in the context of the famous phrase "eat, drink, and be merry." "Joy," by contrast, appears in 60 verses in the New Testament, all of which seem quite positive, including the quintessential Christmas passage: "And the angel said unto them, Fear not: for, behold, I bring you good tidings of great joy, which shall be to all people." "Joy" is also a fine Old Testament word. "Merry," on the other hand, seems to have mostly to do with drinking a lot of wine.
ANOTHER UPDATE: Nina says the Polish Christmas greeting -- "Wesolych Swiat" -- translates as "Merry Holi-days." (She seems to imply that the second word there is something in between our "holidays" and "holy days.") She titles her post "Eat, Drink, and Be Merry," but I note that the New Testament passage with that phrase provokes a rebuke from God ("Thou fool"). Note that I have nothing against partying, by Christians and others. I just don't think it's particularly religious.