Exercise-induced asthma is a well-known and relatively common problem in both children and adults. Like regular asthma, it's more common in children, but is also seen in adults. It's usually worse when breathing cold air. In some people, physical exertion causes inflammation on a cellular level, which causes a partial obstruction of the small airways in the lungs. Since the airways are smaller in children than adults, asthma in general is more common in children. As the airways grow with the child, many children will outgrow asthma as they get older since the same level of inflammation cannot block the larger airways of the adult. Cold air can produce the same inflammatory effect in some people, which magnifies the effect.
Typically, exercise-induced asthma feels like normal asthma while the attack lasts. If you pay attention to it, you don't actually have trouble breathing in, you have trouble breathing out, which is when the characteristic wheezes are generally heard. A typical asthmatic attack looks like somebody taking quick breaths in and struggling over a much longer period to breath out.
Exercise-induced asthma is generally treated first with cromolyn sodium inhalers, which are generally pretty effective. It also helps if the patient ceases exercise and removes themselves from a cold environment.
Having had a couple episodes of exercise-induced asthma, I can attest to the fact that it's a pretty unpleasant experience. Thankfully, I don't have asthma in general, because I wouldn't want to live with that sensation hanging over me all the time.