There are two things at work here. First, the breeze cools you because it is evaporating the water off your skin which is an endothermic reaction. It is why we sweat to cool off.
Second, there is a huge difference in the velocities of the molecules in the air and the wind itself. In an average substance at room temperature, the atoms and/or molecules are vibrating around the speed of sound. Now, that’s a very simplistic statement as it depends on the material, the size of the molecules, they types of atoms, it’s temperature, etc. But in any case it’s much, much faster than the velocity the breeze gives the molecules.
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