The celebration of Christmas as the day Jesus was born is a surprisingly contentious issue. We don't know the day or month of Jesus' birth - modern estimates based on clues from the Gospels range from March to as late as October, but make it clear that he was almost certainly not born in December. The major clues relate to weather, animal husbandry, and the lack of a winter census. Winter weather in Judea was cold and rainy, unsuitable for both travel and tending flocks in fields. Since the Gospels (Luke 2:8) tell us that the shepherds were keeping the flocks in the fields at night to feed at the time of Jesus' birth. The same goes for travel to Bethlehem for a census. Even the Romans probably wouldn't force people to travel in bad weather for annual bookkeeping. Since the winter rains end before Passover and start in October, the shepherds weren't in the fields with their flocks if Jesus was born in December. In the Old Testament both the book of Ezra and the Song of Solomon indicate that December was cold and Rainy, so the evidence against Jesus being born in December is pretty good.
So the question then, is where these celebrations come from? Although I'm loathe to use it as a source, and I don't let my students use it as a crutch, Wikipedia has a good discussion of some of the circumlocutions that some early Christian thinkers went through to justify a December birth for Christ. Sextus Julius Africanus suggested in 221 that Jesus was conceived at the spring equinox, and in 386, John Chrysotom argued that Jesus was conceived in the sixth month of Elizabeth's pregnancy with St. John the Baptist. Other early christian theologians ridiculed the very idea of celebrating birthdays, so it is unclear why these two would try to find some justification for setting the date of Jesus' birth.
Christmas was celebrated by Christians only sporadically and locally in the ancient world, becoming important during the reign of the Emperor Constantine. The reason for the emergence of Christmas under Constantine seems more like one of those conspiracy theories out of Dan Brown's The DaVinci Code than the development of a profoundly religious event. Constantine ruled over a multi-religious empire that had multiple conflicting December/January religious festivals. The most important were the celebrations of Saturnalia, the birth of Mithras, and the rebirth of Sol Invictus. It is hard to imagine that the early Church designated December 25th, also the date set aside for the birthday celebrations of Mithras and Sol Invictus, was a coincidence. Romans exerted a lot of social pressure on Christians to take part in the Saturnalia activities that occurred from the solstice to the new year, and by designating December 25th a day to celebrate the coming of the messiah, the Church allowed Christians to enjoy feasts and exchange gifts. Christianizing the existing pagan traditions allowed the faith both survive and spread. Still, Christmas was not a major and widespread holiday until the 9th century.
If you were expecting the Christmas controversy to end there, you'd be sadly mistaken. Although Christians merrily co-opted the winter festivals of the local traditions they came across, including the Christmas tree, those very pagan traditions that they adopted became a source of renewed debate by the 16th century. Geneva seems to be the location of the first strenuous objections to Christmas and other "Romish festivals and fasts", banning them in 1550, along with all previously held religious holidays other than Sunday observances. It seems that the good fathers of Geneva hand't figured out that the Sabbath had been moved to Sunday by Constantine to coincide with other Roman observances, but they were serious about avoiding Catholic and pagan "superstitions". John Knox and the leaders of the Scottish Reformation similarly denounced Catholic innovations such as "Feasts (as they term them) of Apostles, Martyrs, Virgins, of Christmas, Circumcision, Epiphany, Purification, and other fond feasts of our Lady."
English Puritans also developed objections to Christmas celebrations, providing these arguments against them:
(1.) No time of worship is sanctified, unless God has ordained it; (2.) unscriptural holidays are a threat to the proper observance of the Lord's day because these holidays tend to eclipse the sanctity which belongs only to the Lord's day, (3.) the observance of unscriptural holidays tends toward the super stition and innovation in worship which are characteristic of Roman Catholicism.Any non-Biblical celebrations were a superstitious distraction from the serious business of regular worship, and to be avoided by all right-thinking Christians. Once the Puritans gained political power in England under Cromwell, they abolished Christmas celebrations, so from 1647, no official celebration of Christmas occurred. Things in Puritan dominated colonies in the New World were little different. Christmas celebrations were banned in the Massachusetts Bay Colony starting in 1621. From 1659-1681 people caught celebrating Christmas were fined five shillings, while those caught wassailing were arrested. Boston itself banned public Christmas displays for an extended period of time, scheduling classes in schools on December 25th until 1870. Similarly, Congress regularly met on Christmas day until 1855. Alabama was the first state to declare a Christmas holiday in 1836. The Puritan war on Christmas lasted through 1870 when it became a Federal holiday.
The major source of American Christmas celebrations was the former Dutch colony of New York, which produced festivities having little to do with the Christian tradition, but had a lot in common with German and Norse winter festivals. Santa Claus, in the Dutch tradition, seems equal parts Saint Nicholas and Odin until civilized in the modern form by Moore/Livingston. In England Christmas made a 19th century resurgence thanks to Charles Dickens and Prince Albert. Queen Victoria's Prince Consort was German, and brought German Christmas traditions to his new English family. His practice of giving Christmas gifts to their children sparked a fad of gift-giving in much the same way that people adopt the practices of modern celebrities.
Dickens both promoted Christmas celebrations and showed what Christmas day was like in Victorian England - it was normal to expect that merchants like butchers would be open for business. How else was Ebeneezer Scrooge going to purchase a prize goose from the shop down the street, unless you assume that the butcher was living above the shop and interrupted his family's celebrations to make a sale? The popularity of Dickens' and Moore's work combined with the advertising of the Coca-Cola Corporation and the development of leisure time and consumer culture to produce the modern Christmas holiday season. When conservative Christians rail against consumerism and a "secular" assault on Christmas, they are fighting to preserve a tradition that doesn't really exist, or perhaps trying to establish a closer connection between the festivities and their modern interpretations of Christianity.