Agree (and hopefully add)
I agree that the ram temperature increase is modest (no more than the specific kinetic energy of the air).
There are a coupe of extra factors on skin though, none of which should change as dramatically with windspeed as the perceived windchill discomfort forecast numbers.
If you had a metal skin, being blown by dry air, there would be heat loss to the air by conduction only. As long as the air was blown quickly, so the boundary layer would not reach an equilibrium temperature, the speed of the flow shouldn't have a strong effect on cooling. I reckon this is why there's no significant `windchill' through clothes.
Being blown by damp air, condensation and maybe ice formation can take place. Initially this deposits a small amount of latent heat energy. However, the water/ice coating then cools the skin by conduction much faster than the air. If the delivery rate of water controls the condensation rate, then speed matters.
Evaporation from your non-metallic skin is a big factor (as stated above) - into dry air, energy is lost from your skin to latent heat energy. The evaporation rate should increase a bit with wind speed, I suspect more by reducing the capacity of your hairs to trap a protective warm layer than by enabling a higher evaporation rate.
I suggest that radiative cooling is less important for skin, but does have a small effect, independent of wind speed.