SHORT-ISH ANSWER:

Before the mid-1800s, Christmas celebrations (among those who actually celebrated it) was closer to how the modern Thanksgiving is celebrated. That is, it was celebrated at home with friends and family feasting and drinking. But there was a component to it where people, especially in cities, would hold "open houses" so that their extended friends and family—or employees, in the case of employers—could come by for a snack, and perhaps even receive their Christmas bonus.

With little emphasis on the gift-giving aspect yet, many young urbanites spent the day and evening much like New Year's Eve is still celebrated. When drunken celebrations spilled out onto the street, there could be low level criminal mischief, such as vandalism and fighting. This could often be directed at stingy employers who had failed to have an open house, or came up short with the Christmas bonuses. The troublesome celebrants were in the minority, but, nonetheless, many people did complain about the celebrations, and there were several influential New Yorkers who made an effort to promote the domestic, sentimental, family-oriented celebrations.

With the popularization of the Santa Claus myth in the aftermath of the publication of "Twas the Night Before Christmas" in 1823, an already-emerging gift-giving tradition was given a mascot. The emphasis on Christmas being a "childrens day" soon took hold.

LONG ANSWER:

If you follow the citation in the Wikipedia entry, it takes you to a Bloomberg News article, which, in turn, cites the book The Battle For Christmas by Stephen Nissenbaum. Nissenbaum's book is an excellent work, and well-supported. However, I think because it is commonly cited, it gives quite a warped view of what Christmas was before the mid-19th Century. Nissenbaum's book is an argument that there were multiple traditions being observed on how to celebrate Christmas before the mid-1800s:

One tradition was to observe Christmas in a strictly religious sense. This was particularly true of the Puritans/Congregationalists in New England, as well as of the Quakers in Pennsylvania, New Jersey, and New York. To them, the observation merely meant an extra church service in the morning, before spending the day as usual. Unless Christmas happened to fall on a Sunday, that meant an ordinary full day's work.

A second tradition was to observe Christmas as a family holiday, just as we do today. This was particularly popular in New York and New Jersey, among families who were either part of the Dutch Reformed Church, or who had some Dutch ancestry. Observers of this tradition would also often start the day off by going to church, while the rest of the day was spent much like Thanksgiving - a big feast with the extended family. If not playing host, then you might be the guest at the home of a close friend or relative who lived nearby. There was also modest gift-giving, especially to the children in the family, though this was more variable the further back you go. Dutch New Yorkers usually celebrated St. Nicholas Day earlier in December as the "children's day", and many others used New Year's as the gift-giving day. And, often, there was no gift-giving at all - it wasn't quite yet a tradition set in stone. The main way to celebrate was with food and drink and indoor fun and games.

There was a third tradition, too, which was much more like how New Year's Eve or Halloween are still celebrated in New York City and elsewhere. That is, it was a social, public holiday, particularly in urban areas (at least, outside of New England) with a lot of drinking, dancing, singing, and the like. This was usually how young adults, without nearby family, would spend the day. The celebrations could spill out onto the street, and all the expected disorder and misrule that is associated with New Year's Eve, Halloween, or Mardis Gras went with it.

An added aspect to this third tradition was also the tradition of employers, and local authority figures, to hold "open houses" where they would accept visitors. The visitors would usually be the friends and family of the host, but also an employers' employees, or someone who had some kind of personal connection to the host. This wouldn't have been too different from how, say, a modern-day high school graduation party in the United States is celebrated. There would be a spread of food, the host would chat with all the visitors, and the visitors would pay their respects to the host. In some cases, the host may even essentially hand out door prizes, or Christmas bonuses to their employees who turned up. But at the very least, there would be some free food. The guests would stay for a little while before moving on to the next open house, or before going home to spend the rest of the day with their family.

Sometimes, though, these open houses could end up being personal disasters. Employees often expected their Christmas bonuses, or at least a free meal, on this day, and if they turned up and got neither (or, worse, the employer was out of town or otherwise kept a "closed house"), they might come back later in the day, drunk, and vandalize the property.

Nissenbaum's book, then, argues that the "battle for Christmas" was to do away with the first and third traditions in favor of the second. Unfortunately, it seems that a lot of readers of this book, or lazy internet journalists, take from Nissenbaum's book that most people were observing the third tradition, and a small minority observing the first tradition manipulated the public into settling on the second one. In actual fact, the third tradition--at least, the public, disorderly drunken part of it--was probably the minority observation if you judge by the surviving accounts in diaries and newspapers. There are a lot more people complaining about the revelry than there are people complaining about uptight neighbors who refuse to partake.

And that's not to say that Nissenbaum is wrong--far from it. He's right. It's just that the situation was more like this, which internet journalists don't quite grasp from Nissenbaum's book: Most people outside of New England were celebrating the second tradition, of a domestic feasting holiday, with perhaps a small, well-behaved helping of the third tradition. But there was a minority every year who were disturbing the peace by going overboard in their public revelry. Over time, especially with the emphasis on gift-giving, Santa Claus, and children, the public revelry was confined to the days after Christmas (especially New Year's Eve), while Christmas Day itself became the children's day. The celebrants who preferred the domestic tradition won out.

In New England, the story was pretty much the same, except that it was the first tradition (religious observance and little else) that was more prevalent until after the first couple decades of the 1800s, with minorities who celebrated with the other two traditions. Although that's not entirely true, either: as Nissenbaum points out, New Englanders often made special foods and large meals for the day, too, but they just did it on a regular workday rather than on a day of leisure. But by the 1820s or so, the domestic celebrations, with shops closed for the holiday, began to become prevalent there, too.

Nissenbaum quotes from an article in the January 4, 1787, edition of the Hudson [NY] Weekly Gazette that sums up the situation in New York pretty succinctly during the era:

...[I]n 1786, a newspaper in a nearby community pointed out the same contrast between the different fashions in which New Yorkers celebrated the season: “Some good people religiously observe it as a time set apart for a most sacred purpose,” some by “decently feasting with their friends and relatives.” But others observe the holiday by “revelling in profusion, and paying their sincere devotion to merry Bacchus.” The newspaper went on to rephrase the contrast in metaphoric terms: “in several churches divine service [was] performed,” while “the temples dedicated to the service of merriment, dissipation and folly, were much crouded [sic]; where the sons of gluttony and drunkenness satiate their respective appetites.”

"The scene with these gentry generally concludes about midnight, when they sally forth into the streets, and by their unmeaning, wild, extravagant noise, disturb those citizens who would rather sleep than get drunk."

Another such account can be found in the journal of Rev. Samuel Kirkland, who was a missionary to the Iroquois in upstate New York. He spent Christmas 1769 celebrating with some Anglo-New York locals who lived along the Mohawk River, and described the day this way:

The manner in wch. ye ppl. in yse parts keep Xmas day in commemor'g of the Birth of ye Saviour, as ya pretend is very affect'g and strik'g. They generally assemble for read'g prayers, or Divine service—but after, they [e]at drink and make merry. They allow of no work or servile labour on ys day and ye follow'g—their servants are free but drink'g swear'g fight'g and frolic'g are not only allowed, but seem to be essential to ye joy of ye day.

cont'd...

Followup question: Is there a reputable history book on this topic? Because I would read an entire book on this topic. Sexual Deviancy that upsets puritans is something I'd like to know about.

When were Christmas trees incorporated into these Christmas traditions?