Humidity does in fact affect cars multiple ways. In the case of intake air, it changes the air's density, and more importantly changes the oxygen density (how much available oxygen to burn in a liter of 'air' at a given pressure). As for cooling, humidity in the air changes the heat-transfer properties of the air, which again affects cooling (it makes your car hotter for much the same reasons it makes you feel hotter).
Edit: I'll give you that the car doesn't rely on evaporative cooling like skin does, but still, the heat-transfer properties of humid air are going to be different.
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