Could always rig up a 12v battery to power one of those 12v coolers?
When me and my dad would go for a night, we would have it on at home by a power supply we use for radios to get it cold, then have it on in the car on the way to the site, and every so often turn it on when we were at the site/in the field.
We went camping with no facilities though.
Well, there was a big diesel genny on the field, but we didnt have an extension lead to run to the other extension leads so did without.
I wouldnt be too fussed about electrics though.
You can get a power lead, a proper one that is, which has the right plug on the end, with a fused box on the other end of the long cable and can take about 4 plugs, maybe a few more? They are like £50 though.
Another good reason to have a caravan

My parents book a couple of weeks in advance before they go away for the weekend. There are a few sites that you have to book well in advance for.
Im guessing with tenting sites its the same?