Can as asthmatic's body react to a pressure change or temperature drop without problem?

In control or not? If asthma is controlled then lower atmospheric pressure, as in going to the mountains, should have no adverse effect even though there is less oxygen at higher altitude. On the other hand, cold air is a major trigger of asthma. Increased pressure, as in scuba diving, is dangerous for persons with asthma, uncontrolled or controlled, & may result in spontaneous lung collapse called a pneumothorax.
Yes. Yes, but every asthmatic is different. Some asthmatics find that pressure or temp changes can make their symptoms worse. However, it does not bother everyone with asthma. Still, it is a good idea to always keep your rescue inhaler handy.