Lots of mangods (some of them explicitly sun gods) were born or reborn on this day. Beli Mawr, Mithra, Tammuz, Adonis, Baal ("lord"), Horus, Heracles and Dionysus are a few. Many mangods were born in caves, to virgins, and could look forward to a period of teaching mankind followed by a trial, death and resurrection. This usually led to a father-figure god forgiving humanity's sins.
In some cultures, this astronomical event was mythologized as a battle between light and darkness (which eventually interpenetrated the constructs of "good" and "evil"). The Hopi celebration of Soyal and the Mesopotamian ("Iraqi") celebration of Zagmuk both stress such a battle, and during the Iranian celebration of Yalda, bonfires are used to help the sun grow stronger. Shades of this conflict also appear in the Christian theological argument that Jesus' birth signalled the defeat of Satan.
Celebrating the solstice over 12 days was also popular, as the solar year was (and is) commonly divided into 12 periods. In ancient Babylon, slaves and masters exchanged places and a mock king ruled in the palace. In Italy—where Saturn had once ruled but now lay sleeping near Britain, one day to return and usher in another golden age—gifts were exchanged and a mock king, the Lord of Misrule, reigned. In Greece, the monsters of chaos were said to roam free, playing pranks.
These variations on the theme of moral license and tricksterism may have originated in older rites of human sacrifice, which along with divine births and resurrections also occurred regularly around solstices and equinoxes. In many of these traditions, the victim was allowed for a short time to do whatever he wanted to (sinning, or breaking taboos) before dying. The free-for-all Carnival, or Mardi Gras, may a variation of this, perhaps in preparation for the spring equinox.
In ancient mystery religions, such as Mithraism, adepts were taught a narrative of the religion's founder or god. Newcomers were taught the exoteric, or uninterpreted, version. But once these newcomers were initiated into the mysteries, they were often shown a dramatized version of the narrative (or "passion") and were told the symbolic meaning of it—the esoteric version. Fittingly, Jesus does this, telling the crowds parables but revealing to his followers the parables' secret meaning. Gnostics, most likely the earliest Christians (such as Paul), interpreted the gospel narrative symbolically, as being about the growth of the self*. Because they didn't misinterpret the story as being literally true, they were often initiates of other mystery religions, without conflict.
Early anti-Gnostic Christian apologists had a hard time rebutting criticism that their nascent religion was just another mangod-centered mystery religion. They argued that Satan had copied God's plan and reproduced it around the world in anticipation of Christ's birth, death and resurrection. The big difference, they said, between Christianity and pagan mystery religions surrounding man-gods, was that Christianity was based on a "real" incarnate god. To prove their point, they produced gospels written long after the birth of their religion. Then demagogic bishops sent the faithful to burn pagan and gnostic texts that promoted the spiritual, ahistorical nature of the mangods. The rest is
*This gnostic tradition continued in the West, undercover, as a branch of Alchemy, in which lead and gold were symbols for states of the self, not literal metals. Another form of it is still practiced in Masonry.
BONUS: The God Who Wasn't There, a movie about Christian origins (i.e. paganism, the inclusive type of religion that Christianity robbed blind for every one of its exclusive claims).
SUPER HAPPY WINTER HOLIDAY BONUS: Hitchens drips derision all over Christmas.
DISCLAIMER: I actually like Christmas—as the annual solar holiday it is.