I know about the confederate festivals in Brazil due to the exodus of ~20,000 southerners after the Civil War settling there by invitation of Emperor Don Pedro II. This was after the war, however.
I'm interested in similar communities (and celebrations) formed due to the fleeing of war, especially draft dodgers in recent history, both northerners and southerners during the Civil War and even those fleeing the Revolutionary War if distinct communities still exist somewhere.
The history of Ontario, Canada, is very much tied up with war refugees of the American Revolution. Before the Revolution, Ontario was part of Quebec, but was split into two provinces after the war--Upper Canada and Lower Canada. Lower Canada is modern day Quebec, while Upper Canada became Ontario.
The British government resettled Loyalists from the Thirteen Colonies into Upper Canada, as well as in the Maritime Provinces (and, to a lesser extent, French-speaking Lower Canada). If these refugees could prove their war service, or the war service of their father's, then they were also entitled to free land, which was an impetus for many ex-Americans to go there.
This group of founding Canadians are called the United Empire Loyalists, and were mostly refugees after the war. That's because many, if not most, of them had their land back in the U.S. confiscated by U.S. Congress during or after the war, due to their wartime service in support of the King of England. Some of these Loyalists were even forcibly removed from their former homes in the Thirteen Colonies. Life was hard in the first years up in Canada, since there was little infrastructure outside of Quebec city, Montreal, and Halifax at that point, so some of them returned, if they could, but many others toughed it out and forged a life there.
Numbers vary on exactly how many U.S. refugees went to Canada, but it was somewhere in the ballpark of 75,000-125,000 people.
Any kind of celebration of the anniversary of the founding of Ontario or Toronto, or any of the other towns founded before 1800 (mostly located on the north shores of Lake Ontario and Lake Erie) could rightly be considered a celebration of the history of this American immigrant community. There's also "Loyalist Day", June 19th, the day that the act was signed in 1791 that split Upper Canada from Lower Canada, though it's only really celebrated by people who care about such things as far as I know. There are also statues, towns, schools, and the like named after Sir Guy Carleton, who was tasked with organizing the evacuation of Loyalists out of the Thirteen Colonies to their new homes in Canada. Really, the English-speaking history of Canada is very much tied up in the aftermath of the Revolutionary War.
Any good history book about the founding of Canada or Ontario will cover this. Histories of Quebec, Nova Scotia, Prince Edward Island, and New Brunswick will cover it as well, though those other provinces had some history before the arrival of the United Empire Loyalists, whereas Ontario's history is French Canadien history before the arrival of the UELs. So if you want to do further reading, a couple of good free sources would be United Empire Loyalists: A Chronicle of the Great Migration by William Stewart Wallace, and Our Struggle for the Fourteenth Colony by Justin Harvey Smith. For a more modern source, try Hostages to Fortune: The United Empire Loyalists and the Making of Canada by Peter C. Newman.