Cough like this is usually a sign of bronchospasm or airway inflammation and not an infectious etiology. There are numerous triggers for bronchospasm or reactive airways which may vary from person to person- cold air is one of them. The combination of cold air during exercise may be worse than either one alone.Cold air is also dryer (holds less humidity) than warm air, and that can be a trigger, too. Albuterol or an inhaled steroid like flovent may help, but you need to see a pulmonologist to get tested and get a prescription for either one. Mucinex will not help- the problem is not the airway secretions. You may experience some relief breathing through something that warms and humidifies the air like a mask or balaclava. (yes, I am a physician)