Not all the parks are off limits. Usually they only put up signs after one person (or a couple of people) never pick up and ruin it for everybody. Wherever you buy your dog license, you can ask for a pamphlet on the bylaws and regulations about dogs in your area. St-Laurent is the worst, IMO. If you read their laws, dogs aren't allowed in parks or on lawns, so basically, they expect your dog to "go" on the sidewalk.
Montreal is fairly bad for dogs as a whole. Last I heard, 20% of Montrealers had a dog, compared to 1/3 of Canadians.
Up here in Laval, it's so much more relaxed. Everybody on my street has a dog, and we all tolerate each other and respect each other pretty well. So far, we haven't had any dogs left outside barking all night here, but in the city it happened all the time (even though there were less dogs there).
Anyway, enough hijacking.
It sucks that the laws are so against dogs in every way. It is true that no matter what the reason a dog bites, it's the dog's fault. Even if I don't like it, I never want to lose my babies.