Yep except you couldn't see through the fog. Dry Ice is frozen Co2 so you might also increase the co2 level of the air in an enclosed space. and Norm I believe touching dry ice gives you contact frost bite, not a burn. A block of dry ice has a surface temperature of -109.3 degrees Fahrenheit (-78.5 degrees C). So it can not cause a burn, however like a burn, the result is that moisture is removed from the contact area a rapid rate which actually causes the injury. So basically you freeze dry the contact patch.
You want to make sure the area is well-ventilated. Carbon dioxide is heavier than air, and it can concentrate in low areas or enclosed spaces (like a car or a room where dry ice is sublimating). Normal air is 78% nitrogen, 21% oxygen and only 0.035% carbon dioxide. If the concentration of carbon dioxide in the air rises above 5%, carbon dioxide can become toxic.
All things considered stick with water in your swampcooler.