When I was diagnosed with asthma, I asked the same question about asthma being a killer. The doctor said, "No, asthmatics go wheezing into old age."
That was a comforting thought so I am passing it along.
Yes people can play action sports with asthma. Asthma can range from mild to strong. In very strong cases it can be a killer *if not treated*. But this depends on the individual and level of asthma. You can not compare one person to another. Some people have very light asthma where if they played sports they will be restricted and not play as well but do not need to medicate, others can have a dangerous reaction but be fine if they medicate and some can not take the chance at all because they are not in control with medications.
This is something that ONLY you and your doctor can decide. Your doctor can determine what level of activities can be safe for you. I'd say if your doctor says it's ok and you understand how to reverse it you are safe/ok. If your doctors does not recommend it than I'd say don't do it right now.