|A depiction of the god Saturn, as a god of agriculture and seed, holding the Ouroboros, i.e. the snake that eats its own tail, which is the Greek rescript of the Egyptian snake Apep, who encircles the sun, and does battle with Ra each night.|
In Egypt, in the period 3,100 to 100BC, the Khoiak festival, celebrated from Dec 10 to Jan 8, was the annual holiday celebrating the rebirth of Osiris-Ra, generally speaking.
In Rome, in the period c.400-10BC, Saturnalia was a public festival held from 17 Dec to 23 Dec in honor of the god Saturn.
In c.350, Pope Julius I, declared (Ѻ) Dec 25 to be the “official” birth of the man god Jesus, and therein subsumed the former Saturnalia festival into the new Roman state religion “Christmas” holiday. 
Egyptian | Greek
The Greek god equivalent of Saturn, supposedly, is Chronos. The Egyptian god equivalent to Chronos, and or Saturn, depending, is a bit of a murky subject; the following is one take on this:
“The first man, according to the Egyptians, was Hephaestus [Ptah], who was the inventor of fire. From him descended the sun. After whom Agathodaemon (Ѻ) . After whom Cronus [Saturn]. Then Osiris. And then Typhon [Set], the brother of Osiris. After whom was Orus [Horus], the son of Osiris and Isis. These were the first Egyptian kings. After them, the empire descended by a long succession to Bites, through a lapse of 13,900 years [months]; reckoned, I say, in lunar years of thirty days to each: for even now, they call the month a year. After the gods, a race of demi-gods reigned 1,255 years. Then reigned other kings 1,817 years. After them, thirty Memphite kings, 1,790 years. Then ten Thynite kings, 330 years. Then came the kingdom of the manes and demi-gods. 5,813. The number of years altogether amounts to 11,000; which also are lunar years, that is to say, months. All the lunar years which the Egyptians allow to the reigns of the gods, the demi-gods, and the Manes, are 24,900.”
Here, Eusebius, gives what seems to be a Greek conflated take on the Memphis creation myth, situating Saturn as the father of Osiris, which would loosely equate Saturn to the Egyptian god Geb, i.e. the earth, or Atum-Ra, i.e. the sun, depending. The astro-theology jump from Egyptian Geb (or Atum-Ra) to Roman Saturn, here, however, is lacking in clear explanation. (Ѻ)
In 1980, David Talbot, in his The Saturn Myth, being inspired by the work of Immanuel Velikovsky, cover as shown adjacent, attempted to trace out some of the motifs behind Roman Saturn worship. 
“A Greek ostracon cited by the eminent classicist Franz Boll identifies the Egyptian sun god Ra, not with our sun, but with Saturn.”— David Talbot (1980), The Saturn Myth (Ѻ)
|The view of David Talbot (1980) of how the god Saturn was conceptualized by the ancient Romans, supposedly, as the sun being born out of a mountain.|
Of note, Saturday, the 6th day of the week, is named after the Roman god Saturn, in the sense of “Saturn’s day”.
The following are related quotes:
“In this way antiquity disposes of its sun-gods. The Hebrews turned [the sun gods] into Patriarchs. Adam, Abraham, Israel, were names of Saturn. Edom is Adam; and the ancient usage was to name the nation, the land or city after the chief god. The Greeks made these deities founders of tribes.”— Samuel Dunlap (1858), Vestiges of the Spirit of Man 
1. (a) Movers, Franz C. (1841). The Phoenicians, Volume One (Die Phonizier, Volume One) (86, 130) (arc). Publisher.
(b) Dunlap, Samuel F. (1858). Vestiges of the Spirit History of Man (Israel, pg. 53). Publisher.
2. Mangnall’s Abstract of Heathen Mythology – Hmolpedia.
3. Talbot, David. (1980). The Saturn Myth: A Reinterpretation of Rites and Symbols Illuminating Some of the Dark Corners of Primordial Society (Amz) (txt). . Publisher.
4. Aloian, Molly. (2008). Christmas (Saturn, 2+ pgs). Publisher.
● Saturn (mythology) – Wikipedia.
● Saturnalia – Wikipedia.