you can do virtually anything as long as you take your inhaled 30 minutes prior to open up your airways. I play racquetball, high cardio sport nd I've had asthma since birth.
I think swimming and walking is the best exercise for asthma patient.
As far as aerobic activities are concerned, I run and swim. I don't have problems running or swimming, as long as I use my rescue inhaler beforehand. If I plan to go running and it's below 45 degrees outside, I use my nebulizer beforehand because the cold really bothers me. If you have exercise-induced asthma, I think you can do any sport you want, as long as you're smart about it.
Swimming is great. I've had asthma for two years and that's the best. And yoga too. Nothing too harsh.