COPD symptoms could certainly worsen with weather change, including heat, cold, dry or humid environments. Your mother's case may be similar to patients with exercise induced asthma. In such people,
breathing cold and dry air may trigger an attack. The science behind this may be that the air inside our airways is always warmed and humidified by the surrounding tissues. In a susceptible individual, breathing dry cold air will force the body to produce more shifts in temperature and moisture across the airway, particularly with exercise when there is a geater volume of air that needs to be warmed and humidified. These shifts may trigger an asthma like response. So the scarf may be an excellent idea as she ends up breathing warmer and moist air. Some people use a mask but this may not always be necessary. One other option: she can try to take her inhalers (particularly the short acting ones such as albuterol), about 20 minutes before going out. Walking and staying active is still the best thing she can do for her COPD.