Looking back at Grecian philosophical and mythological history, we find that the Presocratic philosophers were keenly interested in finding which substance constitutes the primordial cosmic substrate. Thales posited water as the ARXH of the universe, while Pythagoras asserted it was numbers; on the other hand, Heraclitus felt that fire was the primeval substance that was the ever-changing and governing force of the cosmos. "Everything is in a state of flux," Heraclitus is often quoted as stating. This "flux" consisted of fire and the "strife of opposites." In this way, Heraclitus accounted for all of the diversity manifest in nature. Certain scholars have called Heraclitus a "fire priest," indicating that he worshiped or at least reverenced the sun. While not every classicist will agree, I think there is some merit to this view and there might be evidence that the Presocratics were also prototypical theologians who were endeavoring to formulate a primitive doctrine of God (as they understood him). Now the significant point to note is that Heraclitus and other early thinkers may have participated in a rudimentary form of sun worship: this point is also evidenced by the myths written about Apollo, Helios, and Hyperion.
One excellent source that I have found for dealing with the history of Greek religion is Gilbert Murray's Five Stages of Greek Religion. On p. 134 of this invaluable reference work, Murray writes that worship of the Sun is implicit, "if not explicit," in a number of ancient Greek documents. It is "idealized by Plato in the Republic, where the Sun is the author of all good light and life in the material world, as the Idea of the Good is in the ideal world. This worship came gradually into contact with the traditional and definite Sun-worship of Persia. The final combination took place curiously late. It was the Roman conquests of Cilicia, Cappadocia, Commagene, and Armenia that gave the decisive moment. To men who had wearied of the myths of the poets, who could draw no more inspiration from their Apollo and Hyperion, but still had the habits and the craving left by their old Gods, a fresh breath of reality came with the entrance of HLIOS ANIKHTOS MIQRAS, 'Mithras, the Unconquered Sun.' But long before the triumph of Mithraism as the military religion of the Roman Frontier, Greek literature is permeated with a kind of intense language about the Sun, which seems derived from Plato"(Murray 134).
Will Durant also provides this information: "In 354 [This date may be off. Others have calculated the time at circa 332 C.E.] some Western churches, including those of Rome, commemorated the birth of Christ on December 25; this was then erroneously calculated as the winter solstice, on which the days begin to lengthen; it was already the central festival of Mithraism, the NATALIS INVICTI SOLIS, or birthday of the unconquered sun" (Caesar and Christ 558).
So I would trace the potential development of Christmas from Greece through Persia to Rome.