"Running Doc discusses diagnosis and treatment of exercise-induced asthma"
Having said that EIA (exercise-induced asthma) seems to be caused by the "sudden inhaling of lots of cool, dry air", Running Doc had three recommendations to make, which you can read about by clicking here. His first advice of changing the workout so that it is less likely to bring on EIA , suggested that the enviromnment of a swimming pool with warm moist air might be a better option than other activities. One thing to be aware of is that the heavy chlorination of swimming pools can also affect people's lungs and even cause tightness of breath.
His other suggestions seem very practical and may just be things you had not thought of. So often when working out, the idea is to do as much and as hard as possible, but you may be able to reduce the EIA by monitoring when it starts and changing your workout habits. Another option is to wear a Cold Weather Mask, which has the benefit of warming up the air before it goes into your lungs. If you into working out and asthma is a problem, the article is well worth a read.