Your statement is true if the humidity levels are below 100%. However, if the atmosphere is at 100% humidity, evaporation cannot occur and therefore the cooling effect of evaporation can't happen. The lower the humidity, the quicker evaporation rate and the greater the cooling effect (until the water is gone, naturally).
There is another caveat to add to this dynamic as well..."traditional cooling". It's the opposite of traditional heating. On a crystal clear cloudless night, objects do typically drop a few degrees below ambient air temperature due to the retained heat within those objects being "radiated" from the surface of the objects and out directly into space. That is how frost _can_ occasionally form on the surface of a car when ambient air temperatures are 33-36 degrees (sometimes as high as 40 degrees) and when the wind is very light.
Heat _flows_ from warmest to coolest and always attempts to achieve a equilibrium. At night, objects on the surface of the earth are relatively warm compared to the temperature in space. Without clouds (especially), some of this retained heat energy radiates out into space from the objects (like your car). The cooling of these objects actually contributes significantly to the cooling of the air itself.
The opposite, of course, is traditional heating where a object can be heated above ambient temperature by a distant heat source (e.g. radiator, fireplace/campfire, the sun). We are all familiar with that.
But, having said that, the difference is small...only a few degrees. And, as pointed out earlier, wind by itself will _not_ make the object cooler (or warmer for that matter) than the ambient air temperature. Actually, wind helps keep the object closer to ambient air temperature. When an object is impacted by traditional cooling, wind warms the object up a degree or two closer to ambient (but never above ambient). When the object contains a heat source (or is heated by radiant solar energy), the wind cools it down a degree or two closer to ambient (but never below ambient).
Clear as mud, right?! :-)