In case of mild cough with no other symptoms you can try to feed your dog honey, which can help his/her breathing. Honey allows for an easier clearance of mucous from the airways, which often occurs in bronchitis. As with most respiratory conditions, your dog should not be exposed to drafts or stay in rooms with cold air. As environment is important, prefer rooms with fresh air and no cigarette smoke. If your dog allows it, you can wrap him in a blanket or apply a shawl to the neck to help maintain body temperature, which helps to fight illness.