The only difference from an actual AC system is that there is no pump and condensor to remove heat from the refrigerant therefore it only works until the water is no longer cool enough.
I built one from ideas I found on the internet, powered by Ryobi batteries (using a 3d printed adapter). I used an oil cooler for the evaporator, and separated the ice/fluid section from the top using insulated foam board. I procured a high flow fan and water pump to move the cold fluid through the oil cooler. It does dry the air (the water collects on the oil cooler, and then drip down into the ice area through a small drain hole in the foam board). I can get some pictures if anyone is interested in the design. The main feature is the separation of the ice/fluid from the cooling fins, it lasts a significantly longer time doing so.
Something that also helps: put the ice in the bottom, but the night before, mix water and RV anti-freeze (which I think is mostly ethanol and eco-friendly), and freeze that. It will stay liquid (which of course you need for the pump) cause of the anti-freeze, so you can pour a super cooled liquid onto your ice instead of room-temp or fridge temp water. Makes the ice last longer.
I found I don't really use it though, for several reasons: as mentioned, getting off the ground to cooler air is usually good enough, it takes up space in the baggage, I am more heat tolerant than most, and it requires prepping and loading into the plane, causing me to be hot and sweaty to begin with.
All told, I think I spent < $150, including the cooler, to put it together.