Why is it that when you have water on your skin and an air current travels over it, your skin gets cold?
Whenever water is exposed to air, the water and air begin to exchange water molecules. By that, I mean that water molecules leave the surface of the liquid water to become water vapor in the air and water molecules that are already vapor in the air leave the air to become liquid water. If the relative humidity of the air is less than 100% (meaning that the air can still hold more water vapor), more water molecules will leave the liquid water than will return to it and the liquid water will gradually evaporate into water vapor. If the relative humidity of the air is greater than 100% (meaning that the air is holding more water vapor than it can tolerate), more water molecules will return to the liquid water than leave it and the water vapor will gradually condense into liquid water.
For a water molecule to leave the surface of liquid water, it needs a substantial amount of energy because it must break several hydrogen bonds which are holding it to its neighbors. It obtains this extra energy from nearby molecules and they become colder. Whenever a water molecule returns to the surface of liquid water, it returns this energy to the nearby molecules and they become hotter. Thus whenever liquid water is evaporating, the water molecules that leave the liquid water are taking away its energy so that it becomes colder. And whenever water vapor is condensing, the water molecules that return to the liquid water are giving it energy so that it becomes hotter.
When your skin is wet and water is evaporating from it, your skin also becomes colder. Blowing additional air across your skin prevents any build-up of humid air near its surface so that far more water molecules leave your skin than return to it. The evaporation then proceeds rather quickly and your skin feels quite cold.