What is the best way to cool your beer on a festival without electricity? I am going to some festivals this year but I still struggle to find the most convenient method to cool my beer there.

I already tried bringing a cool box but it was warm after a few hours the first day in. Digging a hole wasn't such a nice idea either.

What is your best method or should I just embrace warm beer?
A high-end cooler packed with ice can stay cold for five or six days. High-end coolers can get somewhat expensive, they aren't necessary for most people. First thing I would do is get a cheap cooler, not the styrofoam cooler that you might get from a gas-station but, an double-wall insulated plastic one. The way that you pack it will make a big difference in how long it stays cold. 

If you can, bring the cooler down to temperature by sticking some ice in it a day before your trip. For the trip, use the biggest ice that you can, small ice melts faster. You can fill big plastic juice bottles with water and freeze them. You also want to fill as much of the cooler as you can, so fill in smaller spaces with smaller ice. Put a folded-towel inside of the cooler, on top of everything else, to prevent too much cold air from escaping when you open your cooler. The towel should take up the entire surface-area of the cooler and when you grab a beer, only lift as much of the towel as necessary. Avoid opening the cooler more than you have to, so grab everyone a fresh beer at the same time. Of course, try to keep your cooler in the shade.

Without ice, you could take a note from the botijo. A botijo is a ceramic jug, called different things but, used around the world as a water jug. The ceramic is porous so it 'sweats'. And just like a with a person, when the 'sweat' evaporates it cools the container down. I wouldn't put beer in it, it'd go flat and it'd be hard to clean. But you could get a growler, keep it wet, and aim a portable fan at it. I don't know how well it'd work but, it's worth a shot. If the beer doesn't stay cold, at least the fan will cool you off.