Christmas was an Earth religious and cultural holiday that commemorated the birth of Jesus Christ and was celebrated on December 25. While central to the faith of Christianity Christmas had its roots in ancient pagan Earth beliefs and customs as well.
In 2266, a Christmas party was held for personnel in the science labs of the Federation starship Enterprise. Captain James T. Kirk made an appearance, and ended up spending a romantic evening with Helen Noel after they met, danced and he talked about the stars. (TOS: "Dagger of the Mind")
Christmas is the setting of A Christmas Carol, a play in which Data was going to be performing as Ebenezer Scrooge in 2367. (TNG: "Devil's Due") When telling Harry Kim about why he finally confessed to the piloting error that killed his shipmates, Tom Paris joked that "the ghosts of those three dead officers came to me in the middle of the night and taught me the true meaning of Christmas. (VOY: "Caretaker", "Non Sequitur")
While trapped in the Nexus in 2371, Captain Jean-Luc Picard experienced a Christmas – complete with a Christmas tree, presents and dinner – with his illusory children and wife, before being shaken from his reverie and resuming his mission to stop Tolian Soran from destroying the Veridian system. (Star Trek Generations)
Since episodes such as TNG: "Who Watches The Watchers" suggest that Humanity has become largely irreligious, it is possible that Christmas continues in the future as a secularized celebration of family and goodwill, while the traditional Christian observances have faded to a greater or lesser degree. In DS9: "Penumbra", however, Kasidy Yates mentions that her mother would prefer her to be married by a minister. This suggests that some Humans may still have some religious beliefs and that holidays, such as Christmas, may be religiously important to them. In the later Star Trek: Deep Space Nine episode "Strange Bedfellows", Kasidy Yates also tells Benjamin Sisko that she will not participate in a Bajoran blessing ceremony because she did not convert when she married him.
In the same year as the production and first airing of the Star Trek: Voyager episode "Death Wish" (featuring Quinn's brief attempt to hide the USS Voyager by disguising it as an ornament on a Christmas tree), Hallmark released a Christmas tree ornament of Voyager. ("Death Wish" text commentary)