The air we exhale on a cold day is visible because of the formation of dew. Actually, the main constituents of the air exhaled from the lungs, are water vapour and carbon dioxide. The temperature of this air is about 40 degrees Centigrade while that of the outside atmosphere is about 10 degrees Centigrade or less. Cold air cannot hold as much water vapour as warm air. Dew is formed when air is cooled to the point where it cannot hold all its water vapour, so the moisture in it begins to condense forming tiny water droplets. The temperature at which the moisture in the air begins to condense is called dew point. If relative humidity is100 per cent, then dew point is nearly equal to the atmospheric temperature.
On a cold day when we breathe out air with water vapour, it is cooled from 40 degrees Centigrade to less than 10 degrees Centigrade. That is, it is cooled to below the dew point but above its freezing point. Hence the tiny water droplets float in the air and are visible.