No, definitely not. In fact enjoyable exercise is even more important for someone with asthma than for other people. Children with asthma have in the past often been 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. Obviously it is good to have strong breathing muscles, because strong muscles tire less easily. Obviously the way to get strong breathing muscles is to take exercise. Far from being prevented from getting exercise, people with asthma should take as much exercise as they can enjoyably manage. With care and understanding this will be much more than most outsiders think possible.