To start with here's one made by Falmouth-based Christian Topf Design as a gift to its clients in 2007. Very limited in terms of animation, the clip is basically a moving illustration, and rather charming in its way:
Next, here's a 1988 short by Sheila Graber, Toys Will be Toys:
And here we have a characteristically warped festive outing from Cyriak Harris:
Moving swiftly on to something rather more traditional, here's a stop-motion Nativity story made by year 6 six pupils from the Hempstead Junior School in Gillingham:
And now, Walter R. Booth's 1901 trickfilm Scrooge, or Marley's Ghost, the earliest surviving film adaptation of Charles Dickens' work. More information can be found on Screenonline.
And finally, an eight-minute BFI documentary about a form of pre-film animation, the magic lantern show. Not strictly pertaining to Christmas (although A Christmas Carol turns up again), it nonetheless seems somewhat appropriate for the season: