The Delaware River actually froze as recently as 2014, and there was another ice jam in 1996. Historically speaking, David Hackett Fischer's Washington's Crossing explains the conditions at the time well:

A major factor in the winter campaign of 1776 was the formation of ice on the Delaware River. Ice conditions varied by time throughout the Delaware Valley, driven mainly by changes in temperature and precipitation...During the month of December in 1776, the river was in general free of ice, until the region experienced three days of extremely cold weather, December 20-23. Ice began to form on the river near Trenton on December 23. So rapid was its accumulation on that day that Washington expected the entire river to freeze over, and he feared that British and German troops could cross on the ice to Philadelphia. On December 24-25, temperatures rose and the ice broke up on the river. On Christmas evening when Washington's army marched to the water's edge, ice conditions varied greatly from one part of the river to another. Above Trenton large quantities of floe ice in flat cakes were drifting down the river.

I bolded the description of the ice because it seems to conflict with the painting, which shows large, jagged chunks of ice. In fact, the painting was done in 1851 (75 years after the event), so it's possible the painter (Emanuel Leutze) never witnessed ice floes on the Delaware to know how they typically appear (though that's speculation on my part).

Fischer's book also contains daily weather logs kept by Philadelphia resident Phineas Pemberton for December 1776, showing that daytime temperatures averaged in the 30s for the second half of the month (and in the 40s during the first half). Cold, but not unusually so. Monthly statistics from Pemberton's diary for 1758-1777 were also published in the Transactions of the American Philosophical Society, so you can get a sense of what typical December weather was like back then:

"Abstract of Meteorological Tables in the Possession of the American Philosophical Society." Transactions of the American Philosophical Society 6 (1839): 395-98. https://www.jstor.org/stable/pdf/1005334.pdf

Another good source, though not strictly scholarly in nature, is the 1975 New Jersey Historical Commission publication The Christmas Campaign: the ten days of Trenton and Princeton, written by Kemble Widmer, the state geologist of NJ. He explains how ice on the Delaware tends to behave, implying it is not an uncommon occurrence even in present day:

When ice coming down the Delaware meets an incoming tide it piles up at the foot of the rapids called Trenton Falls. It takes only four hours to pile ice five feet deep for nearly half a mile down the river, and across its entire width except for three or four narrow channels of rushing water twenty or thirty feet wide. The ice jam can last almost a week and increase in length and thickness for several days, or it can break up in a day or two as it did in December 1776.

I assume that you are talking about Emanuel Leutze's painting Washington Crossing the Delaware, which is part of the collection of the Metropolitan Museum of Art, in New York?

Interestingly, that painting was not actually painted in the United States, but rather Düsseldorf, Germany. It also was not painted particularly close in time to 1776, having been completed in 1851 (though the one in the Met is actually the second version of the painting, the first having been destroyed in a studio fire, though Leutze eventually purchased it from his insurance company, repaired it, and gave it as a gift to the Prussian government). Anyway, Düsseldorf today is a reasonably large and very affluent financial center, but at the time it was a smallish city of about 30,000 people that briefly became famous for its art academy, the Düsseldorfer Kunstakademie, which incidentally is still in active operation today. A number of Americans studied with the teachers at the academy from about 1838 to 1860 or so, with Leutze and his fellow German-American Albert Bierstadt being the most famous. Many other well-known American painters of the middle of the nineteenth century spent varying amounts of time in Düsseldorf, which was known for a style of painting that married an intense illusionism to Romantic themes. Washington Crossing the Delaware has been interpreted as a very savvy marketing move by Leutze, who wanted to increase his renown with his American audience while also offering a rhetorical support to the aborted German Revolution of 1848, many elements of which modeled themselves after the United States. Leutze and many of his fellow Düsseldorf painters were active in the Revolution, as was the Rhine-Westphalia region more generally (this is somewhat tangential, but the reasons for that are generally seen as having to do with the region's relative affluence and industrial development, the fact that it had only been part of Prussia since 1815, and its experience of the relatively liberal Code Napoleon earlier in the century).

Anyway, so that's all basically background to the painting. Leutze's goal was to create a realistic image that would inspire patriotic feeling on both sides of the Atlantic, something at which he generally seems to have succeeded. The Düsseldorf painters were known for their exquisite attention to even minor details, and Leutze in particular was known for his meticulous approach to his work. He had an exact replica of Washington's uniform sent to him by the War Department, which owned the original. He also had his fellow American, Worthington Whittredge, wear the uniform during grueling sessions posing for the painting, after which Whittredge claims he had to be revived through the forcible application of Champagne (indeed, a party atmosphere seems to have pervaded Leutze's studio during the painting - Whittredge says that he kept a cannon and several muskets on hand, as well as a keg of beer, and that visitors were liable to be greeted with the booming sound of cannon fire upon entering the studio). Leutze used Jean Antoine Houdon's famous bust of Washington, originally executed for a statue in the Virginia State House, for the head, largely because it was based on plaster casts of the man's face taken from life, and was widely regarded at the time as the best likeness of the general. Whittredge also says that Leutze would only permit his fellow Americans (as wlel as one particularly tall Norwegian) to pose in the picture, having determined that the Germans were too small of stature to adequately stand in for robust American figures. It's not clear whether this was strictly true, or just clever marketing on Leutze's part, but it does have bearing on the painting's reception.

Anyway, the painting was a huge success, a smash hit on both sides of the Atlantic. If you've never been to the Met, or if you've missed it when you've been there, I urge you to go check it out. It's enormous, with figures who are larger-than-life-size. It's quite an impressive piece of work. However, despite its success, the painting also received a fairly large amount of criticism as regards its accuracy, right from the get-go. The most obvious "mistake" is that the figures carry a flag that didn't exist in December 1776. If you look closely, there are also some pretty preposterous figures, including an American Indian. Others have criticized the way the figures stand in the boats, which would have been destabilized by such a heroic pose. Many of these criticisms come from later commentators, but contemporaries had their problems, as well. One of them was related to the aforementioned populating of the painting with Americans--many critics were certain that Leutze had used Germans to fill out the scene, and that it was clear that these Germans lacked the stature and character that Americans would have. Another frequent criticism was the highly posed and staged nature of the scene, but that criticism has as much to do with changing artistic tastes as it does with anything. Finally, some critics immediately noticed the river, and said that it looked nothing like the Delaware, but instead looked like the Rhine, the river that passes through Düsseldorf. Scholars have tended to agree that the river in the painting looks a lot like the Rhine. I have been to Düsseldorf, and I have to say that the river really does remind me of the Rhine, though I was there in October and didn't see any chunks of ice.

So, I don't really have a great answer to your question about whether the climate was different in 1776. But what I hope my answer has demonstrated is that the painting was hardly set up to be a close representation of what happened that night, having been painted some 75 years later, in a different city, and for a somewhat nuanced and sophisticated political and cultural purpose (including the promotion of the career of one Emanuel Gottlieb Leutze).

Sources:

Groseclose, Barbara. Emanuel Leutze, 1816-1868: Freedom is the Only King.

Wierich, Jochen. Grand Themes: Emanuel Leutze, "Washington Crossing the Delaware," and American History Painting.

Whittredge, Worthington. The Autobiography of Worthington Whittredge.