Why does your cat have nosy breathing?

Your cat could have a deviated septum, like a human who snores. More likely the nose is clogged, either in the sinus or in the outer nose. Try cleaning the nostrils gently with a q-tip. Some cats just have wheezy, snoring breaths. They usually aren't mouth-breathers because they have taste buds that are sensitive to odors on the back of the tongue.