“Thank God It’s Christmas” was written by guitarist Brian May & drummer Roger Taylor. They both had ideas for a Christmas single around July 1984, and made demos for each of their visions. After listening to them back, they decided that Roger’s song was the best.
The other song, written solely by Brian May, later became his wife Anita Dobson’s song, “I Dream Of Christmas.”
While it’s regarded as the only “official” Christmas song from Queen, it was packaged as the B-Side to Made In Heaven’s “A Winters Tale”, which one could argue is a rather Christmas-y cut.