I was discussing this with our resident mechanical systems guru just a few days ago — really hot, humid weather had some of the HVAC systems gasping, and if you can’t reject heat anymore, the system stops cooling (a basic bit of thermodynamics lost on some people). He was reminiscing about when he could use swamp coolers, in the southwest part of the US.
Evaporation works as a cooling mechanism, which is why we sweat when we get hot, because the molecules that go to the gas phase take more than their share of energy with them — somewhere around 2300 J/g, depending on the temperature. And the energy to change that one gram of water’s temperature by a single degree is 4.18 J, so if I have 100g of water and lose one gram to evaporation, the remaining water will cool by 5.5ºC! (Assuming, of course, no other heat transfer to warm it back up. But hey, we’re physicists. Our cows are spherical and inclined planes frictionless)
You can use this cool things off without ice — put the beverages in a canvas bag and hose it down and let evaporation do the work (the canvas holds on to the water, so it doesn’t just run off). It won’t make the beer frosty, but as long as the water can evaporate, it’ll cool it off some. (rule of thumb — if your cold beverage containers tend to “sweat,” then this probably isn’t going to work very well. But here’s another trick for you, from my navy days aboard the USS Disneyworld — to keep that pitcher cold, fill a tall glass or cup with ice and let it float in the pitcher. Cold but no dilution.)