Is it normal for someone to have trouble breathing when it is cold outside?

Depends: Breathing problems from cold can be cold induced bronchospasm or asthma. Get to the doctor, get tested or at lest checked out and treated.

Not necessarily...: Some people with asthma or COPD may feel short of breath when breathing cold air. This symptom should be evaluated by a physician as there may be treatments that could be helpful. Meantime, covering the nose and mouth when exposed to cold air may also help.