To expand on Eric's answer, a swamp cooler uses the evaporation of water to cool the environment. It works because water turning from a liquid to a gas takes work, which is taken from the air as heat.
However, swamp coolers use water, not ice. The energy required to turn 1kg of ice to water is 334kJ, while the energy required to turn 1kg of water to vapor is 2256kJ, almost 7 times as much. Considering the logistical issues around getting ice, compared to getting water, the extra cooling isn't really worth it.
And, of course, the extra humidity this adds is usually not great, except in specific environments.
Now, how to do this properly:
- Get a cross-breeze going. Assuming you sleep at night, it'll usually be cooler outside. Open two windows (preferably on opposite sides of the home), open doors between them, and get a fan to encourage air movement.
- Examine your bed. Some bed types are better than others for comfort during hot weather. Memory foam, for example, tends to retain a lot more heat than you want. On the opposite end, hammocks basically do not retain heat at all. (Though they do require getting used to.) There are other technologies between those two extremes. (Don't forget to examine your sheets as well.)