You seem pretty well sold - on a syncretic amalgam of stories, lifted off of Dionysus/Bacchus, Mithras, and various Mystery Schools. December 25 is the day of the all conquering Sun (Son), the Day of Sol Invictus aka Mithras. After the shortest day of the year, on December 21st, the Winter Solstice - the Sun 'dwells in the underworld' for the three darkest days of Winter. On the 25th - the Sun 're-emerges from the underworld' and the days grow consistently longer, until June 21st, the Summer Solstice. Hence, the Sun (Son) conquers death symbolically, and brings the bounty of Spring and Summer and provides us all the eternal cycles of life on Earth.
Don't look too closely at all of those re-edited and selected 'Canon' manuscripts and Gospels from the Council of Nicea... You may realize that the Church conquered Pagan religions, by adapting them and the official narrative of the life of Jesus, into a hybrid story. For instance, unlikely that anyone out traveling in December, was very wise. More likely - the actual timeframe of the Gospels, around Jesus birth, would be closer to the Spring (equinox), when Easter is celebrated - a typical time of Pagan celebration, just as the Winter Solstice has long been. The task of the Sages was to take existing times of feast and observance, and then turn them into Holy Days for the new religion.
Emperor Constantine was a Mithras/Sol Invictus Guy... He probably thought that HE WAS the diety. To him Jesus would just have been another incarnation of himself, conceptually. And that is how Christians went from being a persecuted Roman minority, to the persecuting Roman majority. Hence - the Pope's hat - is called a Mitre... Named in the days of Mithras.