Hiking, swimming, etc. are good. You need to build up your lung capacity and utilization. This will strengthen your entire respiratory tract. Exhale forcefully through a small drinking straw into a large bottle of water. This forces the bronchial tubes to expand somewhat and become larger.
Some asthmatics have problems when they breathe too deeply.
One way to minimize exercise-induced asthma is to wear a mask that retains heat and moisture and limits the effects of cold, dry air. Spend a few minutes each day practicing standing tall, expanding your chest, and breathing deeply. Move out to the country where the air is purer. Practice breathing through your nose rather than your mouth. Avoid worry and fear.