Just a few of the Gatekeeper's observations . . .
"In the sixth month, God sent the angel Gabriel to Nazareth, a town in Galilee, to a virgin pledged to be married to a man named Joseph, a descendant of David. The virgin's name was Mary. The angel went to her and said, "Greetings, you who are highly favored! The Lord is with you." (Luke 1:26-28)
So Gabriel came to Mary, who was probably around 15 or so, in the sixth month. That, on the Jewish calendar, would be the month of Elul (which has 29 days in it). The month of Elul seems to be around August-September on our calendar. Counting down nine months from Elul (assuming of course everything about the pregnancy was normal except for the whole immaculate conception), would bring us to the month of Sivan, making Jesus a June baby, unless it was a leap year.
This would make sense since the shepherds were with their sheep outside when the angel appeared to them in the fields (And there were shepherds living out in the fields nearby, keeping watch over their flocks at night. Luke 2:8). Just sayin', . . . it was nice and warm, not December like temps.
Luke 2 . . .
"Mary was greatly troubled at his words and wondered what kind of greeting this might be. 30But the angel said to her, "Do not be afraid, Mary, you have found favor with God. 31You will be with child and give birth to a son, and you are to give him the name Jesus. 32He will be great and will be called the Son of the Most High. The Lord God will give him the throne of his father David, 33and he will reign over the house of Jacob forever; his kingdom will never end."
34"How will this be," Mary asked the angel, "since I am a virgin?"
35The angel answered, "The Holy Spirit will come upon you, and the power of the Most High will overshadow you. So the holy one to be born will be called the Son of God. 36Even Elizabeth your relative is going to have a child in her old age, and she who was said to be barren is in her sixth month. 37For nothing is impossible with God."
38"I am the Lord's servant," Mary answered. "May it be to me as you have said." Then the angel left her.
Of course, it really doesn't matter which month He was born in, since Jesus is the reason for all seasons. Merry Christmas!