The hairs on your skin keep a thin layer of air trapped around you. This layer of air is roughly body temperature (98.6 Fahrenheit or 37 Celsius) and quite humid.
Moving air that is either lower temperature than this, or less humid, will replace that thin layer with air that feels cooler than you. You need a certain force of wind to blow that thin layer away.
However, if the moving air is hotter or more humid, then you essentially get the opposite effect, like in a convection oven, where you are pelted with even hotter-feeling air.
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