There’s two reasons a wind cools you down.
Firstly, when you don’t move around, the heat of your body warms up the air right next to your skin and it will start to feel warmer against your skin. Wind continuously replaces this air with colder air. If the ambient temperature is above your skin temperature, this doesn’t happen.
Secondly, your skin always has some moisture on it. Moving air increases the rate of evaporation of that moisture which cools you down because water turning from liquid to gas requires energy. The same phenomenon explains why you feel cold after a shower when your skin is wet.
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