While the Bible never gives an exact date (day, month and year), there are some general indicators of both the year and season of the year. Obviously the exact date of Christ's birth is not needed for salvation, because the apostle Paul specifically told Timothy he had what was needed for salvation—the Scriptures he had learned since his youth (the Old Testament) with the added understanding of faith in Jesus Christ as the Savior (2 Timothy 3:15). Let's look at the general information, though, that is given.
First, let's start with the season of the year. Luke 2 describes the circumstances of Christ's birth. Verse 8 says there were shepherds living out in the fields with their sheep at that time. Various sources will point out that shepherds around Jerusalem would not stay in the fields past the autumn. They would bring the sheep in for the winter.
For example, according to Celebrations: The Complete Book of American Holidays, Luke's account "suggests that Jesus may have been born in summer or early fall. Since December is cold and rainy in Judea, it is likely the shepherds would have sought shelter for their flocks at night" (p. 309). Similarly, The Interpreter's One-Volume Commentary says this passage argues "against the birth [of Christ] occurring on Dec. 25 since the weather would not have permitted" shepherds watching over their flocks in the fields at night.
Also, Jesus' parents came to Bethlehem to register in a Roman census (Luke 2:1-4). The Romans would have known better than to have taken such a census in the dead of winter, when temperatures often dropped below freezing and roads were in poor condition for traveling. Taking a census under such conditions would have been self-defeating.
So from that passage of Scripture we can at least know one season when He was not born—the winter.
So was He born in spring, summer or autumn? A prophecy in the book of Daniel is helpful here. The last part of chapter 9 gives a prophecy about His coming and verse 27 mentions a "week" of His confirming the covenant, but that in the middle of the week He would bring an end to sacrifice and offerings. The book of Hebrews explains how His sacrifice ended the need for the Old Testament sacrificial system (chapters 8, 9 and 10).
A "week" in prophecy can stand for seven years, a day for a year (Numbers 14:34). We therefore conclude that His ministry lasted 3 1/2 years, with the other 3 1/2 years to be completed at some other time. We know Jesus Christ was killed at Passover time and that His ministry started when He was around the age of 30 (Luke 3:23). Putting all of this together makes it most probable that He was born six months before Passover—or sometime in the fall.
An autumn birth is also substantiated, and in fact more positively proven, by the timing of the birth of John the Baptist. Luke 1 tells that story.
John the Baptist's father, Zacharias, was a priest of the order of Abijah. In King David's time the priests had been organized to serve at various times—a week at a time from Sabbath to Sabbath starting with the first week in the month Nisan. They would all serve together during the feast seasons. Abijah was the eighth course (1 Chronicles 24:10).
It is a matter of doing the math to realize he was serving around early June, so when he was able to go home to his wife, Elizabeth, so she could conceive, it would have been around mid-June. That means John the Baptist was born nine months later, probably in late March.
Then in Luke 1:26 we're told the angel appeared to Mary telling her she would conceive her Son in Elizabeth's sixth month. So Jesus Christ was six months younger than John the Baptist—meaning He probably would have been born in late September when Jerusalem was crowded with people coming to observe the autumn feasts. This would explain why there was no room for Joseph and Mary at the normal hotels or "inns" near Jerusalem (Luke 2:7).
Now for the year. This has been the subject of some controversy, but again we seem to be able to find some clues. Luke 2:1-2 tells us Jesus Christ was born during Caesar Augustus' reign at the time of the first census when Quirinius was governor. Matthew 2 also tells us that Herod (the Great) was still king immediately after Christ's birth. Since Herod died somewhere around 4 or 3 B.C., and some records indicate Quirinius was ruling in 4 B.C., we believe Christ was probably born in late September of 4 B.C.
Although it's difficult to determine the first time anyone celebrated Dec. 25 as Christmas, historians are in general agreement that it wasn't until sometime during the fourth century. This is an amazingly late date. Christmas was not observed in Rome, the capital of the Roman Empire, until about 300 years after Christ's death. Its origins show that it cannot be traced back to the earliest Christians.