"Swamp cooler" uses only water, not ice (either kind). If your dewpoint is anywhere near 50F, a swamp cooler can need to be cycled like an air conditioner lest it get TOO cold. Like say, Palmdale CA (or even San Jose) or central Colorado. I've been there. If your dewpoint is 77F, the coolest you're going to get is 80 which may be preferable to 95 but your towels will never dry.
Relatively standard practice for commercial kitchens (even in 70-dewpoint areas like DFW) is a swamp cooler to replace kitchen air exhausted by the grease/vent fans. Costs almost nothing to run, although there are seasonal maintenance requirements-- higher with harder water.
According to some documentation on the history of airconditioning, outside air blowing over a bucket of ice was the first working model. At the time ice was fairly expensive, being harvested from the great lakes/elsewhere during winter and warehoused with-- you can imagine-- shrinkage.
It's also possible to use air alone as a refrigerant. But it doesn't undergo a state change so it's impossibly inefficient.