2yr old has dry hacking cough, since november. Dr confirmed lungs clear. The same thing happens each year in winter. Would a humidifier help?

Yes. It sounds like your child has an irritated respiratory tract. It 's great the lungs are clear. A vaporizer or humidifier often helps in winter months when the humidity is low. Also, you may want to try a dose of Diphenhydramine at bedtime (like benadryl). If the cough continues or worsens, check back with your doctor.
Depends on humidity. Heating systems bake the air & reduce the moisture content. If the humidity drops below the 35-45% comfort range, headaches, dry cough & nose bleeds are common. Above 50% you promote dust mite growth & above 70% increases mold growth. A humidifier/vaporizer that can push the moisture content into the comfort zone helps most kids or adults.Too much moisture is a problem.