What you're describing is thermal conduction.

Every article on wind chill will tell you that it's what the temperature feels like due to the wind. The rate of thermal conduction is what causes "wind chill", but the wind chill itself, derived from the rate of thermal conduction, is how it feels when you're out in the wind at a given, cool temperature. In fact, if you look at wikipedia, the mention this:

"Many formulas exist for wind chill because, unlike temperature, wind chill has no universally agreed upon standard definition or measurement. All the formulas attempt to qualitatively predict the effect of wind on the temperature humans perceive. Weather services in different countries use standards unique to their country or region; for example, the U.S. and Canadian weather services use a model accepted by the National Weather Service. That model has evolved over time."

Of particular interest:

"the temperature humans perceive"

So, how it feels is certainly part of the formula for wind chill, and not even fully agreed upon by every country, unlike the rate of thermal conduction itself.

There was an outside chance that one of my Navy assignments was to go to the South Pole.
In preparation for that I looked up the wind chill factors so that I could have my cameras
ready by changing out the lubrication to keep them functioning. More than that I had to
know what extreme cold would do to me under those conditions. Hypothermia is a very
real threat not only to the camera but also to the photographer. So for those of you who
are foolish enough to ignore how easy it is to get frostbite or worse here is a wind chill
chart to give you what you need to know. This also applies to people who do aerial
photography. With digital cameras cold will increase your battery drain disproportionally
which is one more reason to know before you go into the cold.
Note that frostbite can occur in 15 minutes or less in the blue section of the chart.