Canada was not a country, nor did it have its own army. While Indigenous peoples of Canada did help the British army fight the Americans (and eventually burn down the White House), it would not really be accurate to say that Canada, a mere colony, was at war with the United States in the War of 1812.
Yeah, I am Canadian and I love the War of 1812, and it would be inaccurate to say "Canada" fought that war. Canadians, sure, but the nation involved was the UK.