I see those things occasionally at thrift stores or antique malls. I think they probably used some sort of wick and not ice: like little swamp coolers but I would not bet my life on it.
You see quite a few of those auto swamp coolers at vintage VW shows. I think they were popular in the mid to late 1950's. They worked well out west, but not so well in the South. When you have high humidity, evaporative cooling doesn't work so well.