People with asthma should definitely exercise. Enjoyable exercise is even more important for asthma sufferers than for other people.
Often in the past, children with asthma were asked to sit on the sidelines whilst their classmates played games and did sports. This is completely wrong if there is any reasonable way in which the child can be made fit enough to take part.
What is true for children is also true for adults.
Asthma attacks are hard work. One of the dangers in an asthma attack is fatigue, which may make you weaken in your fight to breathe. Strong breathing muscles are important to avoiding fatigue, and the way to get strong breathing muscles is to exercise.
So, far from being prevented from getting exercise, people with asthma should take as much suitable exercise as they can enjoyably manage.
With the right help, advice, training, treatment, and self-discipline the problems can usually be overcome.