Canada was originally created when 10 colonists from Hyrule (who were beavers) came over to "the new world" (which is actually part of the same world). The colonists made Canada, but Hyrule refused to give up control of the land. When the Hyrulian Civil War took place, East Hyrule offered freedom in return for military support.
Canada sent in five of their ten thousand soldiers. This made East Hyrule moi moi angry, but they promised freedom, and they gave it to Canada. Canada was its own independent nation.
This was ultimately pointless however, because ten minutes after they earned freedom, RobotnikClause took over. He was the official ruler of Canada. RobotnikClause started the First Robotnik War, and went into hiding.
Canada was in chaos, but it actually established a good government now that RobotnikClause was gone. They bombed West Hyrule, as it was still in the Hyrulian Civil War. West Hyrule and Canada began fighting a never-ending struggle of constantly bombing each other.
Bowser has since used his influence to reestablish RobotnikClause as ruler of Canada and forcefully enrolled Canada as a member of the Bowser Empire.
During the First Food War, Canada was battled at many times and RobotnikClause was asleep for the entire battle. Many people were dying and houses were blowing up. During the final battle, the Koopa Bombs sent by Bowser to get revenge on all the sides caused tremendous economic damage, annihilating vast swathes of land in Quebec, Ontario and eastern Rupert's Land. What is left of Canada is currently ruled by a French guy. RobotnikClause was also rumored to have died in the war, but that might not be true.