Oh good grief. If the US invaded Canada the war would be over before the Canadians had a chance to notice there was a war.
All joking aside (and I love Canada and think it's fantastic) it simply would not be a contest at all for the US military. That's not a slight against Canada, it's just a fact.
The Iraqi army and government fared terribly against the US when they invaded.
It would be foolish to describe what came next as success or winning for the United States.
Any attempt to actually occupy Canada by the United States would be absolutely brutal.
This is a literate, technologically advanced and socially cohesive group of people.
Furthermore the geographic setting would mean that the United States would have to spread itself extremely thin or allow resistance to crop up in areas outside their narrow sliver of occupation.