The tradition of telling ghost stories at Christmas time is a moderately long one, and – certainly outside the US, where Hallowe'en has often only become a big thing in the last 20-25 years (very much true where I write, here in the UK) – it significantly antedates current conventions.
The key shaper of the Christmas ghost story tradition was Charles Dickens, who for years published an annual ghost story in December, the most famous, of course, being A Christmas Carol, in which Scrooge is visited by three very frightening ghosts. There are more than 20 of these tales in all, and, given Dickens's stature as a writer, they proved very influential.
Dickens loved terrifying tales, having been chilled as a boy by the bedtime stories told by his nanny, Miss Mercy – Dickens biographies tend to make much of the impact that her "Captain Murderer" tale made on him, 'which she fiendishly accompanied “by clawing the air with both hands, and uttering a long low hollow groan.”' He was also heavily influenced by childhood readings of The Terrific Register, a "wonderful magazine" and precursor to the later Penny Dreadfuls. (I wrote on the Wonderful Magazine genre here.) These periodicals, he wrote, made him "unspeakably miserable, and frightened my very wits out of of my head.”
It's hard to trace the Christmas ghost story tradition back before Dickens, but as to why he fixed on Christmas (not a major public holiday until he laid his hands on it) for his tales, Vic Zoschak suggests that he was tapping into an older tradition, dating back at least to the late 16th century, associating ghosts and winter.
Dickens's Christmas ghost stories have been collected and republished: Ghost Stories, edited by David Stuart Davies, London: Collector’s Library, 2009. A good guide to the genre is Andrew Smith's The Ghost Story, 1840-1920: A Cultural History (Manchester University Press, 2010).
For many people Dickens's most effective and most frightening ghost story is "The Signalman," which is readily available online - for instance here. I don't suppose he'd mind you reading it aloud this Hallowe'en, rather than waiting for Christmas.