FWIW my kids get a cough from now until spring that is Asthma related, it sounds awful but not contagious and doesn't bother them but I am forever explaining about it and it drives me nuts.
OMG same!!!! I'm not offended at all if people ask me about DD's cough. Unless like one kindy mum last year who made a comment that I shouldn't send to my DD to kindy with bronchitis. It's asthma NOT bronchitis.

Anyway if your friends with her then I think its fine to casually bring it up in conversation? Of course your a nice person and your not going to demand that she keep him home or go to the doc but I don't see the harm in saying something like 'oh poor X with a snotty nose is he ok' or 'does he have a bit of a cold' kind of thing?