The reason that having a fan blow air over you makes you feel cooler is that the moving air facilitates evaporation of the sweat. Evaporating sweat is how we cool down when it's hot. The air that the fan blows at you is at the same temperature whether the fan is on or off.
Hanging damp cloths in front of the fan will in principle cool the air down, again as the evaporation (this time of the water in the cloth) will cool the air.