I think this is the principle:

We use evaporative coolers to cool our homes in the Southwest. This works very well because the air here is so dry. When the humidity goes up, they don't work as well, since the air is already saturated with moisture.

The priciple: When water evaporates, it absorbs heat from the air.

A large volumn of air is directed through a pad soaked with water. As it passes through the pad, much of the water evaporates, absorbing heat, and dropping the air temperature at the same time. The "now much cooler" air is directed into the cars interior.