Surely the combined air molecules that are hitting your skin have the same temperature and possibly even more due to the increased kinetic energy?
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Put a wooden spoon and a metal spoon in your fridge for some time then feel them on your skin, the metal spoon will feel much colder, despite both spoons being the same temperature (the temperature of the fridge). Now why is that?
Your body doesn’t sense temperature, but rather it senses *change* in temperature, which we like to call *heat flux*.
This heat flux depends on several factors, most notably the *temperature gradient* (the difference in temperature between the two objects). If you left the metal soon in your freezer instead of your fridge it will feel (unsurprisingly) colder.
This effect is less apparent in the wooden spoon because it’s an *insulator*. An *insulator* resists *heat flux*, reducing heat transfer and thus your sense of hot/cold. This is why we’re not constantly shivering despite the ambient temperature being lower than 37C/98.6F. Our clothes act as *insulators*, and so does the air sticking to our skin.
Wind essentially removes the *insulation* by replacing the air sticking to our skin with cold ambient air, increasing the *temperature gradient* and thus *heat flux* which our body senses as being cold.
This can also explain why wind doesn’t make you feel colder when the ambient temperature is too hot. If the wind is replacing the air on your skin with air that’s even hotter, then you won’t feel any cold. It’s also why cold water can actually feel pleasant if your hand feels “frozen” after handling something cold from the freezer for some time.
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