December 25 is a time for Christians to celebrate Jesus's birth.
The first time Christmas is known to have been celebrated was in 336CE during the reign of Roman Emperor Constantine. But even before Jesus's time, the Romans had long been celebrating in late December.
Saturnalia was a festival from the 17th to the 23rd of December in honour of the god Saturn. It involved continual partying and gift-giving.
Dies Natalis Solis Invicti, the Birthday of the Unconquered Sun, was celebrated on December 25. Although many gods were worshipped, the Sun God was the official god in the Roman Empire, and virtually everyone participated in these festivities. A cult popular among the Roman military, Mithraism, celebrated this day as the birthday of both the Sun God and of Mithras.
The Sun God was a particular favourite of the Emperor Constantine. Roman coins bearing his image have a Sol Invictus image on the reverse, symbolizing that the Sun God rules in Heaven and Constantine on Earth.
Romans weren't the only people that celebrated in late December. Nordic people for instance decorated trees, burned yule logs, and hung holly, mistletoe, and other decorations.
Though it seldom snows there, December in Jerusalem is a cold and wet time. From early Spring to late Fall, it was common for sheep, goats, and cattle to graze on the grassy lands in the area. But after the Fall harvest, animals would be kept close to home where they could eat hay and be sheltered at night.
That any shepherds would be out in the fields, tending flocks at night in late December is very unlikely.
While not explicitly condemning the practice, the Bible hardly encourages the celebration of birthdays. The few times that birthdays are mentioned, they are unpleasant events such as the presentation of John the Baptist's head as a birthday present.
The Bible records the date and time of Jesus's death, but not of his birth. There are sufficient clues that one can make a reasonable estimate though.
Elisabeth conceived (John the Baptist) immediately after Zacharias finished his Abia priestly duties (Luke 1):
 ... priest named Zacharias, of the course of Abia ...  ... he executed the priest's office before God in the order of his course  ... as soon as the days of his ministration were accomplished, he departed to his own house.  And after those days his wife Elisabeth conceived ...
Her cousin Mary conceived (Jesus) six months later:
 And in the sixth month the angel Gabriel was sent from God unto a city of Galilee, named Nazareth  To a virgin espoused to a man whose name was Joseph, of the house of David; and the virgin's name was Mary.  And, behold, thy cousin Elisabeth, she hath also conceived a son in her old age: and this is the sixth month with her, who was called barren.  And [Mary] entered into the house of Zacharias, and saluted Elisabeth.  And Mary abode with her about three months ...
course of Abia is defined in the First book of Chronicles:
[24:10] The seventh to Hakkoz, the eighth to Abijah [24:19] These were the orderings of them in their service ...
Each priest served for a week, with the cycle beginning on the 1st day of Nisan. But during the week of Passover (Nisan 14) and Pentecost (7 weeks later) all priests served together, so Zacharias, being of the 8th course, would have finished his first course after the 10th week of the year. Six months after that (Jesus's conception) would have been around what the Romans called late December, and nine months after that (Jesus's birth) would have been late September or early October.
That would be around the time of Sukkot (the Feast of Tabernacles).
Sukkot is one of three times each year when people made a pilgrimage to Jerusalem.
In addition to the normal tithe given to support the priesthood, people were encouraged to save a second tithe to use for their own expenses and celebrations during these times (Deuteronomy 14:26):
And thou shalt bestow that money for whatsoever thy soul lusteth after, for oxen, or for sheep, or for wine, or for strong drink, or for whatsoever thy soul desireth: and thou shalt eat there before the LORD thy God, and thou shalt rejoice, thou, and thine household.
Even today, most people that observe this fall festival travel away from home, or if they can't, they arrange to sleep in a tent or some other location different from their normal home.
It's by no means a certainty that this is when Jesus was born, but if Jesus had been born during the Feast of Tabernacles, it then confirms why his parents stayed in their family's home town of Bethlehem, just south of Jerusalem.
Roman Christianity was developed during the first few centuries after Jesus, and was largely canonicalized during the reign of Emperor Constantine. Though he was largely responsible for defining Roman Christianity, throughout this process Constantine remained a Sun worshipper, and didn't formally convert to Christianity until shortly before his death.
One way for the official Roman religion to subsume the many existing religions and cults, both in Rome and throughout the Empire, was for it to incorporate their more popular practices while requiring nothing more than that the names be changed. A single universal religion, regardless of what it believed, would make the Empire stronger and easier to control.
If people wanted to continue to celebrate December 25, whether in honour of Mithras or of the Sun God Apollo, they could continue to do so, just so long as they now call him Jesus.