My husband has PGM ancestors to moved to Canada (Quebec and Nova Scotia) because they were loyalists, and some chose to do so because they simply wanted to avoid war. Some of the latter headed to less populated areas in New Hampshire, Vermont, and upstate New York from Massachusetts. I am not suggesting that everyone who moved to Canada was a loyalist, but that was a relatively common reason why they did so.
You could look up what americanancestors.com or ancestry.com has for loyalist records. I personally have found reading local histories (understanding that most books were written well-after said events took place, some data may not be well sourced, but it can still make for a good jumping off point) is a good place to find some of those details.
One book I read a few years back on the history of Barnet, Vermont listed mentions of people who came through town or calls for militiamen to arrest or route loyalists.
If you know where your ancestors lived or where they may have migrated (possibly in order to avoid persecution from patriots), you may find some details on your specific family(ies).
Hope that helps.