Putting a hole into the chest releases the negative pressure in the thoracic cavity. Such injuries are obvious, but many other respiratory diseases can be more insidious. Remember, any reduction of airway diameter has profound effects on air flow. Inflammation is characterized by swelling so that inflammation of air passages creates constrictions for airflow. Damage to the facial nerve can reduce the ability of the nostrils to dilate and they can collapse.
Horses are obligate nose breathers, so such collapse is a true problem.
Inflammation of the nasal sinus, sinusitis are a common problem with many etiologies of upper respiratory tract disease. The pharynx is a relatively large space, compared to other structures in the airway but pharyngitis, if severe enough, can impede airflow. Pharyngeal lymphoid hyperplasia is a condition that is not uncommon. Here lymphoid tissue swells and can create inspiratory noise. Diagnosis is by endoscopy.