In Canada, the war of 1812 is seen as a victory because American invasion attempts were repulsed. In 1812 and 1813, U.S. armies, often with a large numerical superiority attempted to overrun Ontario or Quebec, but were beaten by a handful of British regulars supported by local volunteers.
Next year will be the 200th anniversary of the Battle of Chateauguay where a British/Canadian force of 1500 defeated an American Army of 4,000 attempting to capture Montreal.
As to why Canadians stayed loyal to the Crown, 80-90% of the population was made up of Catholic French-Canadians. The most important local insitution at the time was the Catholic Church. The Church trusted the British who in 1763 had granted religious freedoms to Catholics, maintained french civil law and, more importantly, guaranteed the status of the Church.
The Church did not trust the U.S.A for a variety of reasons: fear of any revolutionary movement, especially after the excesses of the French Revolution; and fear of American protestant religious zealots which were (and still are
) influential on the U.S. Government.