basically when you turn a fan on its not pushing cold air against your face its just re-circulating the hot air. i think iif your sweating it helps cool you down by increasing the rate of evaporation.
But it still feels cooler when you have no moisture/sweat on your skin.
I thought it may have to do with it " pushing " the warm air molecules away and off your body and replacing them with normal temperature air molecules.
A moving air stream has lower pressure than the surrounding air. Therefore the air will actually cool very slightly as it expands. Not sure if you could feel the difference in temp though.