Why moving air feels colder than still air?

This is the wind chill factor and the answer to this is a bit like saying 'I'll turn the fan on.' Does it make a room colder? No! A fan running does not cool a room. A running fan keeps the room at the same temperature, it just moves more air past you. Air molecules, when they run past you, if you're sweating and hot, each molecule can take a little bit of heat away from your skin so the more molecules that pass your skin the more heat you can lose. It makes you feel cooler but it doesn't actually affect the temperature and that's why when you're driving along nice and fast with your window down, lots of air molecules running over you cools you down.