I couldn't end this series without including one of these.
It doesn't have to be anywhere near Christmas when you play it, either - they generally shoot them around July and August, and The Next Doctor is about the Doctor visiting Christmas because he wanted a bit of cheering up.
(These are actually more often the start of a new series filming block, and included in the DVD box set for the series that follows next year, but never mind.)
X: Get Away From The Christmas Trees!
Christmas Specials are by and large seasonal big-budget hour-long variations on classic Who themes. They're pretty much one-shots, but advance the emotional story, sometimes introduce significant new characters and drop in references to upcoming arcs. The Christmas Invasion is... you can probably guess. The Runaway Bride is a screwball chase comedy happening in the middle of a slight alien invasion (and in introducing Donna becomes a retroactive Season Opener). Voyage Of The Damned falls into the deliberately-wide-enough-to-include-it Format-Bender category, being a somewhat parodic but fairly straight disaster movie that happens to involve people from space and killer robots, because The Big Christmas Movie is a TV tradition here. The Next Doctor is a Pseudohistorical Secret Invasion with the addition of raising questions about the Tenth Doctor's mortality. The End Of Time is an exception to most of the format, a Series Finale that happened to be set around Christmas, joining the noble tradition of stories that use the setting as an ironic backdrop to a story about separation and loss and death and rebirth. Let's throw in The Unquiet Dead as well, a Celebrity Historical that directly ties in to the foundations of the modern British view of the holiday, and manages to be enormously Christmassy despite the potential zombie apocalypse and being broadcast in May.
Christmas has plenty of opportunities to be emotional, funny, scary, weird, ironic, depressing, uplifting, sometimes all together over the space of an hour. Many and many a year ago (eight) I put an article on RPGnet about Christmas Specials for games, so take a look at what I said here and see what applies. (Note that most of these links are long dead and I have since discovered to my relief that A Very Star Wars Christmas never really happened.)
And there should be snow. Even though it's never actually snow. (And The End Of Time didn't have any because it was shot in autumn, but shown during the snowiest Christmas we've had in decades.)
Oh, and while evoking the Nativity would be apt, getting in the TARDIS and visiting the actual event is unlikely to get past BBC Standards & Practices.
Example: The Gift
Visiting home from her voyages across space and time, one of the travellers arrives in time for Christmas with her extended family, but her presence draws in a young refugee from the destruction of an alien-sponsored program to create human psychics. A mashup of The Little Match Girl and Scanners ensues with the addition of two warring bands of aliens sneaking around the house, a bit of door-slamming farce as everyone attempts to hide the psychic and the aliens from each other and from the traveller's very ordinary family, and since it's Christmas at one point the psychic opens the walk-in freezer and creates a snowstorm in the kitchen to block one of the alien groups chasing her.