Could exercise prevent asthma?

No. Exercise improves exercise tolerance, but does nothing to help asthma. That being said, it does not worsen it either.
Yes. If you don't have exercise-induced asthma, or you treat it appropriately, exercise can help with your general wellbeing and thus help your asthma. Asthma has a large psychosomatic component. If you feel well and not stressed out, you are less likely to suffer from asthma.