If you are diagnosed with EIA there are several effective treatments. In addition to the cold, dry air that Ryan mentioned another common trigger, especially in spring time are the common alergens like pollen and ragweed.
I have EIA and began using AdVair, a preventive taken twice a-day, since mid November. Since then I have not had any symptoms while running, or otherwise for that matter.
Out of fear I still take an emergency inhaler (Albuteral) with me while running but have not used it. I guess the idea of having an attack while miles from home still worries me a little. As time goes by and I gain confidence in the AdVair I will no longer need the Albuteral.
Only a doctor can determine what will work best for you. AdVair is only one of many available medications. If EIA is causing your breathing problems I’m sure you can find a treatment that will be effective and allow you to run freely.