Actually, we do know the time of year He was born, and we've got a good idea of the day. Luke gives us the clue we need (Zechariah's priestly order) to know the time of John's conception (mid-summer) with just a bit of study in the Judaica, and tells us point blank that Yeshua's conception was six months later. It should also be noted that John, who came in the spirit and power of Elijah, was probably born on Passover, the time of year when we set out a cup for Elijah in the expectation of his reappearance.
We do know for a fact that Yeshua was not born in December, because it rains, sleets, and snows in the Judean mountains during the winter months, so the sheep of Bethlehem would have been closed up in pens, not out in the fields with their shepherds.
Roman law was a bit fluid about when to collect taxes, especially if a census was involved, because they had to allow time for individuals to travel. In this case, registration may have been due by January, but there's no reason why Joseph and Mary, on their way to Jerusalem for Sukkot, wouldn't have stopped off in Bethlehem to register on their way (Bethlehem being only six miles south) to get it over with instead of traveling during the rainy season three months later.
Sukkot, the Feast of Booths, makes sense as the birth-date: It is the most joyful of the Feasts, and has the theme of celebrating God dwelling with His people. Tradition tells us that the construction of the Tabernacle began on Sukkot, and 2Chr 5:3 tells us that the inauguration of the First Temple, when the Divine Presence came to dwell in it, took place on Sukkot. It lasts for eight days (really, seven plus a bonus day), which would neatly correspond with Yeshua's birth and circumcision on the eighth day.
And finally, there was absolutely zero reason for the very-pregnant Mary to travel along with Joseph if they were only going for secular tax registration. On the other hand, if the event coincided with a pilgrimage Feast, it makes sense that the Messiah's earthly parents would want to be extra-scrupulous in observing all the Feasts.
While I can't say with 100% certainty that Yeshua was born on Sukkot, I can say with 100% certainty that He wasn't born on Christmas, which was originally a pagan holiday celebrating the winter solstice. He was probably conceived close to what is now Christmas, however, which may be why the early Church began adopting and altering that holiday.
I've thought that April 1st would be His birthday and since Satan hates God so much, we call it April Fools day!!
I'll investigate further.
Feast of Booths also called the Feast of Tabernacles. John 1:14 And the Word became flesh, In the Greek dwelt is Strong's G4637 - skēnoō
There is a hint(Remez) in John 1:14 shalom b'SHEM Yah'shua HaMashiach Adonai
and dwelt among us,
and we saw His glory,
glory as of the only begotten
from the Father,
full of grace and truth.
1) to fix one's tabernacle,
have one's tabernacle,
abide (or live) in a tabernacle (or tent), tabernacle
2) to dwell
John 1:14 And the Word became flesh,
In the Greek dwelt is
Strong's G4637 - skēnoō
It can be determined by finding out when Zachariah was doing his priestly duties in the temple. It was the "course of Abia" Luke 1:5-8. Now Elizabeth got preggers then and 6 months later, Mary got pregnant. 9 months later Jesus was born. Through a long and intricate study, we find when the course of Abia, or "Abija" in some translations, was,( in the OT), and add 15 months you get Tabernacles.
Now that is just facts we can deduce from the Bible.
In the symbolic realm, Tabernacles celebrates the "Light Of the World". A pole has swaddling cloth wrapped at the top dipped in oil and is lit. The priest declares "Behold the Light of the World", as he points to the lit pole in the courtyard. Tabernacles is the only Jewish Feast for the whole world. Jesus came for the whole world. All others are for Jews only. In John 1, we see the Word was in the beginning, the Word was with God and the Word was God, clearly meaning Jesus. In verse 14 we see, "And the Word became flesh and dwelt among us, and we beheld His glory, the glory as of the only begotten of the Father, full of grace and truth." The word "dwelt" there is actually the word "tabernacled", and is the only time in the Bible it is used in that fashion. There are many more reasons to believe Jesus came to us on Tabernacles, but these are the most convincing. Each time a Temple or Tabernacle was built for God to "dwell" with His people, it was dedicated on Tabernacles.
On a side note, you hear many Christians and Jews talking today about rebuilding a new Temple on the Temple Mount. If that temple is built it will be for or by the Antichrist. Revelations tells us that the Second Coming of Christ will be the New Temple building time. Jesus will first re establish the Sabbath on Saturday, and bring with Him the plans for the New Temple.
Well before the pagans attached themselves to the winter solstice, it was set in motion by the Heavenly Father. And given we are given details regarding when John was conceived and how old in the womb he was when Christ was conceived, how hard can it be to count. It makes perfect sense that on the shortest day of sunlight that the Light/Life Giver would begin His life in flesh. Emanuel = God with us.