When your skin is in contact with still cold air, your skin and the air near the skin eventually reach the same temperature: warmer than the surrounding air, but cooler than the skin might otherwise be.
This is because when the temperature of your skin is lower than ‘normal’ you experience a sensation you call ‘cold’. If the warmed air next to your skin is removed (by the wind) then you will lose more heat as you start to warm a lot of new air. Eventually your skin will reach the temperature of the air.
The speed with which your skin cools down depends on the wind speed.
This increase in the speed of heat transfer is sometimes characterised by a ‘wind chill’. For example, an air temperature of 3 °C and a wind speed of 10 metres per second (about 22 miles per hour) will cool you at the same rate as being in still air with a temperature of -3 °C. The improvement of heat transfer by blown air is also experienced in reverse in a fan-assisted oven. The cold food cools down the air immediately next to its surface. By continually removing this cooled air and replacing it with hot air, the speed with which the food reaches the temperature of the oven is reduced.