What is the best way to cool your beer on a festival without electricity?
That will depend on on several issues.
First of all some beers may be better served at warmer temperatures than other beers.
Depends on the beer really. A good rule of thumb is darker beer should be served at a warmer temperature than lighter beer.
For instance if you refrigerate all of your beers and then pull them out of the fridge and drink them instantly you will miss A LOT of the flavor complexity of pretty much every stout and porter you put to your lips.
But, if you let the dark stuff warm up for just 15 minutes before you drink it (let it sit at room temp) a bunch of new flavors will appear that you never would have noticed otherwise.
This doesn't work so well, in my experience, for lighter beers like pilsner, lager, or hefe-weisen. They really are meant to be drank cold and letting them get warm changes their flavor profile for the worse.
Obviously there will always be personal preferences but, at a minimum I encourage you to try letting your darker beers warm up just a bit and see what a positive difference it makes. - What temperature should I serve my beer?
Another possible idea is that if you are near water you can get a Floating Cooler For River or Pool. They range from 6 cans to 72 cans.
Intex Mega Chill II Inflatable Floating Cooler, 48" X 38" holds 72 cans.
Then of coarse there is the traditional cooler method. The larger the cooler and the more ice there is in it will keep your beer warmer.
There is also a Coleman Thermo-electric 12V Ice Chest which may serve your purpose. This what I when I go camping. No ice is recommended. You have to pre-cool the cooler at home and then plug it into the outlet in car or truck. keep the chest plugged into your vehicle the whole trip to your destination. One fall back to this system is that you can not leave plugged into your vehicle more than 3 hours without the car or truck running. But then you can either take an additional cooler or floater with you.
Coleman 40 Quart Power Chill Thermo-electric Cooler is what I use and it works great. Use it with darker beers and give it a try. Do not open it every 5 minutes and recharge it in the car every so often. It works like a charm.
If you are lucky there may be a cold natural spring near by to place your beer into.