It is my understandoing that some asthma is also strictly cold induced, regardless of exertion based on what I was told concerning my son years ago.
And just to add a different twist to demoncyclist's advice concerning a pulmonologist... If you have any additional symptoms, you may want to see an allergist.
I developed Cold Urticaria, which is an allergy to cold.
http://www.coldurticaria.info/ There are other symptoms along with breathing... I first discovered mine in August when I was holding a can of Pepsi for several minutes and my hand started itching severely. When I looked online to see possible causes (since it had never happened to me before) I realized that I had experienced a couple of other symptoms, but had ignored them.
I use Singulair daily, Zyrtec twice a day, and keep Albuterol and an EpiPen close by just in case... especially when it is cold. So far I haven't needed the emergency measures even though I regularly go for walks, regardless of temp, a couple of times a week. The allergist insists that I don't go on the walks alone, but that works for me since I am always with at least one other person.