The relative humidity at high altitude is extraordinarily low, and almost invariably irritates the respiratory tract. The result is the infamous “Khumbu cough”, which can be serious enough to cause a person to cough hard enough to break a rib.
The best way to prevent it is to wear a mask that heats and moisturizes the air you breathe. A balaclava worn especially at night may be helpful. Many climbers use masks that can be found in cross-country ski stores. These masks have a metallic net inserted in a lightweight plastic or cloth shell and were originally developed for the Finnish Olympic ski team.