Rome borrowed most of its mythology from its conquered people, primarily the Greeks. However the Saturnalia has strong roots in the central Egyptian mythological story.
The Sun-god Osiris and his consort, Isis, together with Re-Atum, the "Father of the Gods," were regarded by the ancient Egyptians as the supreme rulers of a Golden Age of plenty called Zep Tepi or the "First Time." Their kingdom ended abruptly when Osiris was murdered by his evil brother, Seth. The childless Isis searched for the dismembered body of Osiris, which she then reassembled and resuscitated long enough to conceive a son named Horus. Horus was believed to be the reincarnation of Osiris, and the new husband of Isis, whose destiny it was to repossess the Kingdom of Osiris from the control of Seth.
The tradition of the Christmas tree symbolically portrayed the death and reincarnation of Osiris in his son, Horus:
The Christmas tree, now so common among us, was equally common in Pagan Rome and Pagan Egypt. In Egypt it was the palm tree; in Rome it was the fir; the palm-tree denoting the Pagan Messiah, as Baal-Tamar, the fir referring to him as Baal-Berith. The mother of Adonis, the Sun-God and great mediatorial divinity, was mystically said to have been changed into a tree, and when in that state to have brought forth her divine son. If the mother was a tree, the son must have been recognized as ‘Man the Branch.’ And this entirely accounts for putting the Yule Log into the fire on Christmas Eve and the appearance of the Christmas tree the next morning. As Zero-Ashta, ‘The seed of the woman,’ ...he has to enter the fire on ‘Mother night,’ that he may be born the next day out of it, as the ‘Branch of God,’ or the Tree that brings divine gifts to men.
Alexander Hislop, The Two Babylons or The Papal Worship, Loizeaux Brothers, 1916