Have you ever wondered, why does wind feel 'cold'? Whenever you stand in front of a fan or even simply waved your hand in front of your face on a hot day, wind is generated.
Temperature is a feature of all matter, be it a small molecule or a large plane, everything has temperature. Wind is simply moving air, hence it has temperature. The movement of air does not exactly make the air colder-it just makes us feel colder.
Wind helps us feel cooler in 2 different ways: evaporation and convection. Our bodies naturally regulates temperature through a multitude of ways, one being sweat. When the sweat on our skin evaporates, the heat transferred from our body into the sweat gets transferred yet again into the air, removing heat from our body. A fan blows wind at us, replacing the still air around our body that is filled with humidity from the evaporated sweat with dryer, cooler air. This 'new' air will allow for the evaporation of our sweat to occur more efficiently, cooling us faster.
The second way a fan can cool us down is simply via convection. Even without sweat, heat from our body is naturally lost to the surrounding air by convection. When our body temperature is higher than that of the surrounding air, heat is transferred from our hotter body to the cooler air. However, in still air, the hot air surrounding you will be trapped, forced to slowly diffuse out. A fan creates wind that blows away the hot air, increasing the efficiency of convection, cooling you off.