It’s actually because of evaporative cooling. Your body releases small water molecules through skin pores all the time. Even at the same temperature the dry wind sucks some of the fastest moving (hottest) H2O molecules thus cooling you down. That’s why hot dry air feels cool but humid hot air does not.
When there’s no wind your body heats up the air that is touching you. There is now a area around you that is warner than the rest of the air. This air insulated your body and you loose heat more slowly. When there is wind that warmer air is removed and replaced with woolen air that can cool you more quickly.
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