When we blow on/stir a hot drink, why aren't we making it hotter?
This is related to a concept called "vapour pressure". Liquid water (and any other liquid for that matter) always has some amount of water vapour that has to be in equilibrium with it. For example, the air above water of 5 °C has about 1% of water vapour, 40 °C has about 7% of water vapour and at 90 °C it has about 70% of water vapour.

If there is too much vapour in the air for the temperature it is, then water condensates. That's why you get condensation on your glasses when you walk from a hot humid room outside into the cold at winter. If there is not enough vapour in the air, water evaporates to fill in for the missing vapour. That's why taking off your shirt after you've exercised and sweated makes you dry faster. The air trapped between your skin and clothes is very humid and in equilibrium with the sweat on your skin. Once you take it off, dry air comes into contact with the skin, forcing evaporation of your sweat (even though you're below the boiling point of water).

This process of evaporation is endothermic, meaning it consumes heat. Whenever water is evaporating, the temperature of the water goes down. When you're blowing air on a hot drink, you're basically replacing the humid air on top of the drink with dry air. This allows the water to evaporate more easily, reducing the overall temperature of the drink. This is also why you're feeling cold when you got wind blowing on your when you're sweating.