This is all to do with how you lose moisture from the surface of your skin. This is one of the ways in which your body regulates your body temperature. So if there is a movement of air around your skin, it is more effective at removing the moisture and so you feel cooler.
Solid surfaces, like our skin, loses heat through evaporation, conduction, and radiation. How much heat is lost by conduction depends on the difference in the temperature of our skin and the air around it. As our skin heats the air a layer of warm air forms around us. The wind then blows this warm layer away and our bodies have to heat up the cold air now surrounding us all over again. This means we lose more heat and feel colder.
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