Can going out in the cold without a jacket give you a cough?

Unlikely but: breathing cold air can induce a cough for people who have some inflammation in the airways. If you do cough with cold air, see your doctor to make sure that you don't have a mild case of asthma. If you are a smoker , then this may be the explanation. Going out in the cold without a jacket gives you a shiver not a cough if you are otherwise healthy.