I cough when I step outside because of the temperature differential and environmental allergies. While I would prefer to not bark like a harbour seal, it's impossible to stop. I can muffle by coughing into my elbow, but if I tried to staunch it, I might end up tossing my cookies.
People make people sounds while living in apartments. If they're right next to your window or something, you might be ok asking them to move over a bit to decrease the noise. Otherwise, you might just have to deal.
Generally I agree that you can't ask them to stop; them's the breaks of apartment life, as you said. But, if they're standing right outside your window, and there's room for them to stand farther away from your window, I think you could sometime mention something like, "Oh, hey, neighbor, I was wondering if you guys could stand farther away from my window in the future? Sounds carry so easily through it and things like talking, the dog barking, etc. wake me up in the middle of the night." I wouldn't mention the coughing just because they really can't help doing that, but maybe they could not
hang around your window so much.