Why December 25? Because The Romans held a festival on December 25 called Natalis Solis Invicti which marked the birth day of a solar deity called Sol Invictus or Mithras. There's a beautiful temple of Mithras, in Merida, Extremadura, Spain.
Sol Invictus is Latin for The Sun Undefeated - as he survived the shortest day, the Winter Solstice.
In the Vatican is a 3rd century mural of Christ as Helios, the Sun God.
Who is Father Christmas? The traditional Father Christmas was neither a gift bringer, nor associated with children. He has his roots in Paganism.
By the time of the Anglo-Saxons in England (around the mid-5th century AD), it was customary for an elder man from the community to dress in furs and visit each dwelling.
At each house, in the guise of "Old Winter" (or "King Frost" or "King Winter"), he would be plied with food and drink before moving on to the next. It was thought he carried the spirit of the winter with him, and that the winter would be kind to anyone hospitable to Old Winter.
The tradition was strengthened when the Vikings invaded Britain (during the period from the late 8th century to the 11th century) and brought their own midwinter traditions with them; these involved the god Odin, traditionally represented as a portly, elderly man with a white beard.
The custom was still kept in Medieval England, after a decline during the Commonwealth under the Puritans.
Christmas itself was banned by Puritans between 1647 and 1660.
The custom became widespread again during the Restoration period. Father Christmas was also a significant character in Christmas Mummers' Plays.
A book dating from the time of the Commonwealth, The Vindication of Christmas, depicts Father Christmas advocating a merry, alcoholic Christmas and being cynical about the charitable motives of the ruling Puritans.
During the Victorian era, he was merged with "Old Winter", "Old Christmas" or "Old Father Christmas", and the charitable Saint Nicholas, a Greek Orthodox Saint (or Dutch one, depending on the version). This character did give gifts to children.
In 1863, a caricaturist for Harper's Weekly named Thomas Nast gave Santa a "flowing set of whiskers" and dressed him "all in fur, from his head to his foot." Nast's 1866 montage entitled "Santa Claus and His Works" established Santa as a maker of toys; an 1869 book of the same name collected new Nast drawings with a poem by George P. Haddon identified the North Pole as Santa's home.
In 1931 Coca Cola helped popularise this already existing, portly, sack-wielding image of Santa in a successful advertising campaign, but did not create the image, as they would have you believe.
Perhaps it's time to return to the roots of Christmas, and away from the modern consumer frenzy, which is hardly compatible with either Christianity, paganism, or sustainability.