" Now I remember those old women’s words,
Who in my wealth would tell me winter’s tales,
And speak of spirits and ghosts that glide by night”
The Christmas ghost story was (and to an extant, is) a British tradition more than an American one, but one that most of us still take part in to a degree. The most famous Christmas ghost-story is Charles Dickens' "A Christmas Carol in Prose, Being a Ghost-Story of Christmas" (1843), which has been adapted innumerable times for the stage, radio, television, film, etc., but the tradition was alive in well into the 20th century with the likes of M. R. James, whose volumes Ghost Stories of an Antiquary (1904), More Ghost Stories of an Antiquary (1911), A Thin Ghost and Others (1919), and A Warning to the Curious and Other Ghost Stories (1925) all follow the same pattern; James himself wrote in the introduction of the first volume that most of the stories "[...] were read to friends at Christmas-time at King's College, Cambridge[.]"
Just as some of these stories were set into print, in the 1920s and 30s the written stories became adapted to radio, and finally television, as detailed by Derek Johnston in Haunted Seasons: Television Ghost Stories for Christmas and Horror for Halloween:
In 1928, E.F. Bendons read his ghost story The Confessions of Chales Linkworth, and the following year took part in a Christmas Eve broadcast called The Haunted Hour, alongside W.W. Jacobs and Desmond MacCarthy. In the 1930s, this presentation of authors reading their own stories disappeared, although it returned on Christmas Night 1939, when Algernon Blackwood told his stories 'Transition', 'The Laughter of Courage' and 'A Boy and His Bag'. The rest of the 1930s saw the continued significance of A Christmas Carol, including the multiple performances of the role of Scrooge by Bransby Williams, who had first appeared as the character on radio on Christmas Day 1929 and would ocntinue to do so until 1944. These appearances moved to television as part of its first Christmas celebrations in 1936, providing connections between the familiar radio and the new medium.
Television and radio productions of ghost stories around Christmastime continued, though Johnston notes that they decreased during WWII, and that while a recognizable tradition it was not one maintained consistently - he goes into much greater detail on individual broadcasters and programs, if you're interested in digging deeper. These broadcasts have continued fairly into the present, with the most famous being the BBC series called A Ghost Story for Christmas from 1971-1978, which was revived in 2005.
Most of these ghost stories were not actually set at Christmas time or with Christmas as part of the plot, which might have been part of the reason they lost something of their seasonal appeal to American audiences, but the idea of Christmas-themed horror stories continued with short pulp fiction like H. P. Lovecraft's "The Festival" (Weird Tales January 1925), in horror comic books and magazines, and film and television programs such as Silent Night, Bloody Night (1972), Black Christmas (1974), Gremlins (1984), The Nightmare Before Christmas (1993), Jack Frost (1996), and Krampus (2015).