Can you bring a cat to a public park (in upstate NY, to be specific) where dogs aren't allowed?

I want to start leash-training my cats, but I live on a busy main road where there are too many cars/dogs/people/questionable things on the ground…

ASKED BY Monti on 9/25/13
TAGGED park, leashtraining, leashes, rules, laws, parklaws, publicparks IN Laws & Legislation