Luke 2:10  And the angel said unto them, Fear not: for, behold, I bring you good tidings of great joy, which shall be to all people. 

Luke 2:11  For unto you is born this day in the city of David a Saviour, which is Christ the Lord. 

Luke 2:12  And this shall be a sign unto you; Ye shall find the babe wrapped in swaddling clothes, lying in a manger. 

Luke 2:13  And suddenly there was with the angel a multitude of the heavenly host praising God, and saying, 

Luke 2:14  Glory to God in the highest, and on earth peace, good will toward men. 

Mat 1:18  Now the birth of Jesus Christ was on this wise: When as his mother Mary was espoused to Joseph, before they came together, she was found with child of the Holy Ghost. 

Mat 1:19  Then Joseph her husband, being a just man, and not willing to make her a public example, was minded to put her away privily. 

Mat 1:20  But while he thought on these things, behold, the angel of the Lord appeared unto him in a dream, saying, Joseph, thou son of David, fear not to take unto thee Mary thy wife: for that which is conceived in her is of the Holy Ghost. 

Mat 1:21  And she shall bring forth a son, and thou shalt call his name JESUS: for he shall save his people from their sins. 

Mat 1:22  Now all this was done, that it might be fulfilled which was spoken of the Lord by the prophet, saying, 

Mat 1:23  Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us. 

Mat 1:24  Then Joseph being raised from sleep did as the angel of the Lord had bidden him, and took unto him his wife: 

Mat 1:25  And knew her not till she had brought forth her firstborn son: and he called his name JESUS. 

Calculating the actual date when Christ was born

The Bible does describe the timing of Christ's birth. We can calculate this from context clues given in the Bible. As we know from basic human biology, the average child is born about 9 months after they are conceived. Christ's conception is something announced in the Bible, in the Gospel according to Luke 1:26-38. In these verses we see only one timestamp given: 6 months into the pregnancy of Elizabeth, the mother of St John the Baptist. Mary is informed that she will bear the Son of God and gives her consent to this, and then she conceives. 

So far we have two timestamps: 9 months after the Annunciation, and 6 months after the conception of St John the Baptist. However, we don't yet have an exact date. In the scriptures, though, we are told when St John the Baptist was conceived. The Gospel of Luke 1:5-22 describes the conception of Saint John the Baptist as happening "of the course of Abia"

 This is a critically important point because this describes the jewish holiday of Yom Kippur, which happened in late September of 1 BC. 

How does that simple phrase describe Yom Kippur? Well, the Scripture records the Course of Abia as the eighth course among the 24 priestly courses for the Old Covenant Jews. (Nehemiah 12:17). Each course served one week in the temple for twice each year. The course of Abia served during the 8th week and the 32nd week in the annual cycle. This means that the priestly course of Abia (the course of St Zacharias) was serving during the 2nd week of the Jewish month of Tishri – the week of the Day of Atonement on the 10th of Tishri. In the secular calendar, the Day of Atonement on 10th Tishri lands anywhere from September 22 to October 8. In 1BC, Hebrew Calendars have calculated it to be roughly equivalent to be about September 27th. 

http://www.cgsf.org/dbeattie/calendar/?roman=1bc

Zacharias and Elizabeth conceived John the Baptist immediately after Zacharias served his course. This means that St John the Baptist would have been conceived somewhere around the end of September. 

This confirms the Orthodox Church’s celebration of the Conception of St John the Baptist on September 23, and places his birth 9 months later at the end of June, confirming the Orthodox Church’s celebration of the Nativity of Saint John the Baptist on June 24. 

So if St John the Baptist was conceived around September 23rd-27th, then Christ was conceived 6 months later in March (23rd-27th). That means Christ was born 9 months later in December, 23rd - 27th, which just so happens to contain December 25th. 

"But what about Saturnalia" 

Ultimately irrelevant. If pagans would celebrate the Winter Solstice, it does not affect when Christ was born. He was born exactly when He was meant to be born. Christians had been celebrating the Nativity before they knew of Saturnalia. 

Furthermore, Saturnalia was NEVER celebrated at the same time as Christmas (the Nativity). Saturnalia was celebrated initially on December 17th, and expanded to Dec 23rd, which conveniently does NOT contain Christmas which is on December 25th. 

"But the word Christmas is of pagan origin" 

No it is not. It's etymological origins are "Christ's Mass." (Mass meaning missal or Liturgy) Other names like X-Mas derive from the Greek letter Χ which is the first letter of Christ's name in Greek (Χριστός) 

"But Christians do pagan things on Christmas, like put up Christmas trees" 

Christmas Trees were popularized by protestant Christian reformer Martin Luther, who is said to have put up the first Christmas tree when he placed lighted candles on an evergreen tree. Not pagan at all. While such an act and tradition had nothing to do with the Christians of the first 1500 years, this is still nevertheless a Christian origin to an already Christian holiday. 

Alse the trees are mentioned in the Bible: 

Cedars ( אֶרֶז ) are mentioned, as are Cyprus/fir ( בְּרוֹשׁ ), but in all the searches I can find the mentions are positive (1 Kings 5:8, 10, 6:15, 6:34, 9:11, 19:23; 2 Chronicles 2:8, Psalm 104:17, Isaiah 14:8, 37:24, 41:19, 55:13, 60:13, Hosea 14:5. In fact Isaiah 60:13 talks about these types of evergreens being brought into God's throne room to beautify it. 2 Chronicles 2:8 praises the skill of those who cut down such trees. So if we're in the neighborhood of cherry picking proof texts... 

"But Santa Claus is based on paganism" 

No he is not. While Santa has been sensationalized by western consumerist culture, he still has his origins in Christianity, being directly founded upon Saint Nicholas of Myra, a Greek Orthodox Bishop in Anatolia. This is where the traditions of stockings come from. Saint Nicholas, known for his charity, donated incredible amounts of gold to a father of three daughters who was about to be forced to sell his daughters into prostitution, placing this gold in their stockings. Saint Nicholas gave away everything he owned, and greatly enriched the people wherever he would go. This is where gift giving in connection to Santa Claus is based on. So to say this is pagan in origin is historically illiterate. 

Jesus Dominates The Season Against all gods

1Co 8:1  Now concerning food offered to idols: we know that "all of us possess knowledge." This "knowledge" puffs up, but love builds up. 

1Co 8:2  If anyone imagines that he knows something, he does not yet know as he ought to know. 

1Co 8:3  But if anyone loves God, he is known by God. 

1Co 8:4  Therefore, as to the eating of food offered to idols, we know that "an idol has no real existence," and that "there is no God but one." 

1Co 8:5  For although there may be so-called gods in heaven or on earth--as indeed there are many "gods" and many "lords"-- 

1Co 8:6  yet for us there is one God, the Father, from whom are all things and for whom we exist, and one Lord, Jesus Christ, through whom are all things and through whom we exist. 

1Co 8:7  However, not all possess this knowledge. But some, through former association with idols, eat food as really offered to an idol, and their conscience, being weak, is defiled. 

1Co 8:8  Food will not commend us to God. We are no worse off if we do not eat, and no better off if we do. 

1Co 8:9  But take care that this right of yours does not somehow become a stumbling block to the weak. 

1Co 8:10  For if anyone sees you who have knowledge eating in an idol's temple, will he not be encouraged, if his conscience is weak, to eat food offered to idols? 

1Co 8:11  And so by your knowledge this weak person is destroyed, the brother for whom Christ died. 

1Co 8:12  Thus, sinning against your brothers and wounding their conscience when it is weak, you sin against Christ. 

1Co 8:13  Therefore, if food makes my brother stumble, I will never eat meat, lest I make my brother stumble. 

Acts 17:28

Acts 17:28  for "'In him we live and move and have our being'; as even some of your own poets have said, "'For we are indeed his offspring.' 

1Co 8:4  Therefore, as to the eating of food offered to idols, we know that "an idol has no real existence," and that "there is no God but one." 

1Co 8:5  For although there may be so-called gods in heaven or on earth--as indeed there are many "gods" and many "lords"-- 

1Co 8:6  yet for us there is one God, the Father, from whom are all things and for whom we exist, and one Lord, Jesus Christ, through whom are all things and through whom we exist. 

Col 2:16  Therefore let no one pass judgment on you in questions of food and drink, or with regard to a festival or a new moon or a Sabbath. 

Titus 2:11  For the grace of God that bringeth salvation hath appeared to all men, 

Titus 2:12  Teaching us that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly, in this present world; 

Titus 2:13  Looking for that blessed hope, and the glorious appearing of the great God and our Saviour Jesus Christ; 

Titus 2:14  Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works. 

Titus 2:15  These things speak, and exhort, and rebuke with all authority. Let no man despise thee. 

Research materials on the topic: 

Articles:

• A Christian Defense for the Celebration of Christmas Real Christianity https://podcasts.apple.com/us/podcast/a-christian-defense-for-the-celebration-of-christmas/id1408224071?i=1000541552847 

• Calculating Christmas  The Story Behind December 25 by William J. Tighe  http://www.touchstonemag.com/archives/article.php?id=16-10-012-v 

• CHRISTMAS IS NOT PAGAN By Marcia Montenegro http://www.christiananswersforthenewage.org/Articles_ChristmasNotPagan.aspx 

Satire on the topic