The cough you're describing is called an asthmatic cough. When your cough gets worse in cold weather or exercise, you are having what is called exercised induced asthma. Exercise induced asthma is controlled by using your MDI 15 minutes prior to going outdoors or exercising. (Call your MD about exercised induced asthma prior to starting this type of preventative measure.) Also keeping your neck warm with a turtle neck shirt/sweater will help.
Asthmatics have a tendency for air trapping since you can breathe in, but it's hard to expel. The following is a simple exercise to remove air trapping and allow the oxygen your body needs into your lungs:
Relax your neck & shoulders.
Breathe in slowly through your nose for 2 counts.
Pucker your lips as if you were going to blow out a candle.
Breathe out slowly through your lips for 4 counts.
Hope this info helps.
he information is from Krames on Demand, an information site used by a lot of hospitals & medical offices.