If you're going primitive camping, which means that you're going to be hiking in to your campsite a couple of miles from where you've parked your car, then you're probably not going to have a way to keep your food cold by refrigeration, or a cooler, or ice. The only trick I know, aside from just preparing to bring food that doesn't need to be refrigerated, and the cool thing is that there's food that you think that needs to be refrigerated, but really doesn't. It's just modern convenience that makes us refrigerate everything.
Things like cheese and butter are things that you can get away with, out refrigerating. The only really trick I know for getting food cold or cool when you're camping and primitive camping is if you happen to be near a river. What you can do is put the food inside a plastic bag. Make sure it's completely sealed up. Tie a rope to it, and put the food in the running water. The river is probably cool enough that it'll get your food cool. It's not going to make anything cold, but it'll work for some stuff. If you brought beer, it'll get your beer pretty cool. It'll taste a little better.