In the early Greek periods, December was the month of orgies and feasts and festivals to the gods. It was the time of the feast of Saturnalia. The winter was coming, and they wanted to appease the gods, that they would survive the winter and they would see the spring and all of this. So these tremendous pagan festivals to Saturnalia and to many other deities were held in December. Now, the Constantine Roman Empire that came about in about 300 or so, after that they wanted to sort of Christianize everything, and so in approximately 450 AD the bishop of Rome decided that it would be really good if they could Christianize the festivals of December. So he determined in some kind of conjunction with the Bishop of Jerusalem that they would spot December 25 as the birth of Christ. And if they could pick December 25th as the birth of Christ, that might sanctify all of this, even though it’s highly unlikely that He was born then. They were really trying to overpower the paganism. But instead, they got a mishmash.
Additionally, The biblical narrative of Jesus' birth gives no date for the event, though it more likely occurred in spring than in winter. Saint Luke tells us that shepherds were "abiding in the field, keeping watch over their flocks by night" -- shepherds guarded their flocks day and night only at lambing time, in the spring; in winter, the animals were kept in corrals, unwatched.
The biblical narrative of Jesus' birth gives no date for the event, though it more likely occurred in spring than in winter
How about the narrative in Luke 1:5 where Zechariah, belonging to the priestly division of Abijah(I Chron 24:10)upon finishing his service (2 weeks) in the temple.... verse 24, "after this his wife Elizabeth became pregnant and for five months remained in seclusion." Zechariah's service was the sixteenth division according to the Hebrew way of reckoning and would have taken place about four months after the beginning of the Hebrew year....or about July through August our time.(Four months from the first Hebrew month of Nisan), which corresponds to our April.
If Elizabeth became pregnant around the first of August Mary would have visited her around the first of February, Luke 1:26-45. "In the sixth month...." If Mary became pregnant with Jesus the first part of February then Jesus would have been born in the fall...perhaps around the date of the Feast of Tabernacles.
The Feast of Tabernacles was God's last annual holiday each year and this seems quite fitting to me if indeed this was the case.