Originally, the winter solstice fell on December 25th. (Special day, isn't it) But when the Roman Catholic Church re-engineered the calendar in 1582, one of the many things they did was move the solstice away from the the 25th, separating Christmas from all of the other Solstice celebrations.
Anyway, Saturnalia - the principle celebration of the Roman Empire would run for the 17th to the 23rd. "Io Saturnalia!" was the primary season's greeting.
Saturnalia - by our current calendar it is usually listed as December 17 through December 23. Originally - by the old Calendar - covered the 25th. Besides honoring Saturn, the goddess Ops, goddess of abundance, was celebrated via gifts and feasts - probably on December 19th.
Mithras - Roman god, who was a resurrected god, who was worshiped at Saturnalia, He was supposed to have been born on December 25th. Apparently very popular in the Roman Legion.
Solstice - December 21 by our current calendar, fell on December 25th in the old calendar. Celebrated the return of the light - the end of the shortening of the days, and the beginning of the lengthening of the days.
Yule - Norse and Germanic Solstice celebrations. Usually listed as the official name of Wiccan Solstice celebrations.
And of Course ...
Festivus - December 23, which dates to at least 1966, and is definitely not an invention of the Seinfeld Show, though many of the "traditions" are from that show.
And of course, all these competing holidays have caused confusion for some time... Take a look at the ancient document.
"What's this empire coming to? Now they want us to stop greeting people with "Io, Saturnalia"! "We have all these different cultures in Rome", they tell us. "We shouldn't offend anyone", they tell us. "We should be inclusive."
"We've got the barbarians from the north with their tree decorations and their fire rituals. And the weirdos from Gaul, cutting mistletoe with a golden sickle. And the Mithraists, the Zoroastrians, the Isis cults, and, of course, those characters who hang out in the catacombs. "Hail, Winter!" we're supposed to say. I ask you, what next: we lose the feast? We stop the Solstice parties? No more honoring Ops, goddess of abundance?
"I was buying some candles and greenery down by the Forum the other day, and there's old Macrobius with some Visigoth chick, and she goes, "Gut Jule". So I go, "Hey! In this country, we say, "Io, Saturnalia! Maybe you should go back to where you came from." Then Macrobius goes, "She can't, she's a slave".