If a colder air molecule hits you, it will absorb some heat, thus cooling you down and make you feel cold.
If a warmer air molecule hits you, it will deliver some heat to you, thus heating you up and making you feel warmer.
The air molecules surrounding you will under normal circumstances heat up quickly and then not absorb any more heat from you. You will quickly not be cooled down any more in any significant amount, since the thermal conduction of air is low and the natural convection happening is not that powerful.
But imagine having the touching air molecules replaced constantly. Each will absorb heat from you and then be moved away, giving place for a new one to absorb heat from you etc. The ceiling fan causes this forced convection.
This means that
- if the surrounding air is colder than your skin temperature, then the fan cools you down, while
- if the surrounding air is warmer than your skin temperature, then the fan heats you up.
If you have ever driven through Death Valley in California on a hot summer day, you will agree - one does not roll down the car window, since that only heats up the passengers.
If you sweat, the heat transfer between body and air molecule is faster, so this whole process will be more effective and you will feel even colder. But even without sweat, that effect is still taking place.