EIA can be controlled and lessened. EIA is not solely as a result of an exposure to cold weather. It is more accurately described as sudden exposure to temperature CHANGE. Asthmatics, as people with migraines can be characterized as having a vascular disease.
When it is cold out, the veins constrict to conserve your heat. The skin has a lot of blood flow, so this is why we become pasty white in the wintertime. Conversely, in the heat we can become flush, or red. This is a result of the dilation, as the body moves to cool itself.

During sudden temperature shifts, sometimes the body spasms during this 'transition' period. This can bring on an asthma-like symptom.

To minimize this, make sure that you are well hydrated BEFORE the ride. Even a little dehydration can bring on vasocontriction. (we get 15% of the water in our system from our respiration, so if you don't run a humidifier you might be 15% deficient as you wake up in the morning)

Another way is to be exposed to the cold for about 10-15 minutes prior to exercise (just standing in the colder air, to get used to it could help)

I do know that if your first episode occurs in the 1st 15-20 minutes, once you let the worst of it pass and don't push it, you could minimize the attack and proceed to your harder workout.

then there is all the allergen's and pollution that contributes to it. The chicago area recently had very bad air quality. all the soot and pollution that had been kept in the snow for the last month had been released into the air when it all melted and there was no wind, so everything was sitting there.