When the heating comes on, indoor humidity drops to 20% and the night cough starts

Normal is 40-60%. At 20-25% the lining of the nose dries out, crusts make breathing harder, and by morning there is a cough and a child who keeps waking. It is not a cold: no fever, fine all day.

A humidifier or the improvised equivalents, saline rinses, airing the room before bed, and 18-20C. A cough lasting more than two weeks, or any wheeze - see a doctor.