Probably not. The most common explanation was that He was probably born around the end of September (for more info, here's one source).
So.... if He wasn't born at that time, should we celebrate that date for His birth?
In fact, Christ wasn't even "born" when He came to live on this earth. He existed from the beginning. He is God and has existed in eternity past. When He came to earth, we say that He was incarnate or became a human in the flesh. In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning.... The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the One and Only, who came from the Father, full of grace and truth. (John 1:1-2,14)
Should we celebrate Christmas as a religious holiday? If it's not a religious holiday, why would Christians get so upset that people want to say "Happy Holidays" instead of "Merry Christmas?"
Some people believe that we shouldn't celebrate any religious holidays because 1) we don't know the exact date and 2) we celebrate His life, death, and resurrection every day.
Don Fortner wrote:
We must not observe any religious holiday. We should attach no spiritual, religious significance to any day. Yet, we do not need to act like super-pious religious idiots over a day that has absolutely no religious significance....Did you know that every DAY of the week, every PLANET in the universe, and many of the CARS we drive are named after pagan gods? Yet, we still call Sunday Sunday, Mars Mars, and a Saturn a Saturn. No one would ever dream of calling us pagans for doing so. We worship our God on Sunday, and would laugh at anyone who suggested that we observe the pagan Roman holiday called “Sun’s Day” in doing so. If your car is a Saturn, use it for the glory of God; and laugh at anyone who thinks that you are worshipping the Roman god of agriculture by driving it. We must not, and I trust do not, worship Christmas trees and lights, or even attach spiritual significance to Christmas day.
However, I do suggest that we seize this opportunity afforded us by Divine providence to tell people who Christ is, why he came into this world, what he did, and how they may obtain his salvation. It is no accident that once every year every human being in the world is confronted with the fact that the Son of God assumed human flesh and came into the world to save men. Certainly, no one can think that it is wrong for believers, during this season of the year, to express thanks and praise to God for his unspeakable gift, the Lord Jesus Christ. It is never wrong, but always right to think of Him, speak of Him, and sing His praise. Rather than not singing Watts’ grand old hymn, "Joy To The World," we ought to sing it year round.
For me, yes, we will celebrate Christmas. Christmas is important to our family as one expression of our faith, our traditions, and the memories that go with them.
The Christmas celebration will not be more worshipful than other days. The tradition will not be the foundation of my faith.
However, the hearts of so many people are very tender at this time of the year. It gives us great opportunities to share why we believe, to share our hope and our future.
The Christmas message is that
there is hope for a ruined humanity –
hope of pardon, hope of peace with God, hope of glory –
because at the Father’s will
Jesus became poor, and
was born in a stable so that thirty years later He might hang on a cross.
J.I. Packer
