Anything you can do to increase your aerobic capacity is a good start. Also, try to breathe through your nose as much as possible. Mouth breathing is colder and drier. You can also wear something to keep the warm air in- a buff or bandana over your nose and mouth can be helpful. Are you on any meds? My asthma isn't exercise induced, and if you have only seen a GP about this, he may be incorrect in his assessment. Go see a good Pulmonologist and be tested to get the full picture about how good or bad your breathing is and get any meds you need to keep the inflammation in your lungs under control. I take Singulair and Claritin daily as controllers and always have an Albuterol inhaler within arm's reach.