Yes, I imagine that the statistics for dog related breathing trouble are much lower than those for cigarette related trouble, because fewer people will have dog trouble than cigarette trouble and there are generally more smokers than dogs in a pub!

I can't speak for others but, as a rule of thumb, if I can't smell something, it's probably not going to trigger my asthma (so dog in a park, or cigarette in a park = not big deal). But if I can smell things (strong perfume, smelly animals, cigarettes), there's a jolly good chance it will make me ill.