Old fashioned "air conditioning" -- Does this work?

[JayhawkSD]

7. Actually. that's not quite accurate

Swamp coolers work with water at ambient temperature, which is allowed to evaporate. As the water changes from liquid to vapor the "latent heat of vaporization" required to accomplish that is absorbed from the air and thereby cools the air flowing over the evaporating water. Air flowing over a block of ice is merely being cooled by the cooler air surrounding the ice, by a process called "adiabatic heat transfer." The ice is sufficiently cold that the localized effect is noticeable, but significant cooling of actual air mass is a great deal less than that accomplished by a swamp cooler.

It does indeed require low humidity, or the water will not evaporate. Air passing over a block of ice will be pretty much equally effective (or ineffective) regardless of humidity, because evaporation is not involved.