You don’t really feel a temperature. You feel the effect it has on your body temperature.
Your body is constantly generating heat, and it has a few ways of getting rid of excess heat. If it can’t get rid of heat fast enough, you feel warm. If heat is bleeding away too fast, you feel cold.
Part of bleeding away heat is that you heat up the air around you. As that air heats up, you decrease that temperature differential, so you hit some sort of equilibrium.
If there’s a lot of wind, then that air around you is going to get replaced much more frequently. You don’t really have a chance to reach an equilibrium, so you are losing heat as if the temperature was a few degrees cooler.
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