If we exhale in the cold environment, water vapour condenses into little droplets, so we can see it. Why does this condensed cloud disappear so quickly? What happens to it ?
Moist exhaled air is at body temperature; when it begins to mix with cooler ambient air, the low partial pressure of water at ambient temperature means that the moisture will form droplets (because it started at higher concentration/partial pressure than cool air allows).
The droplets, then, diffuse with your exhaled breath into a larger volume than your lung volume, and those droplets are in cool and dry ambient air. So, they evaporate. Slowly at first, when volume per drop is high, and surface area is relatively small because of square-cube discrepancy, but faster when the droplets are smaller.
One liter of air at body temperature and 95% relative humidity contains 0.04 grams of water. At 0 C, one liter of air at 99% relative humidity contains 0.005 grams of water, so you might expect up to .035grams of condensation. At 0C, and 50% relative humidity, it takes 14 liters of cold air mixed with your exhalation to evaporate that condensate.