Insulate the dry ice by wrapping it up with newspaper. You want to keep it dry as much as possible. Wetting dry ice activates it into steam and evaporates it. Also know that if you put a can of pop into a cooler with even a little uninsulated dry ice, it will explode. Your cooler will be more of a freezer than a fridge.
So insulation of the dry ice itself determines how long it will last and how cold the cooler is. No insulation of the ice will freeze the heck out of everything but shorten the life of the ice. Heavily insulating (and keeping it dry) will lighten the freeze factor and extend the life of the dry ice.
Hope this helps. I used to deliver foods to restaurants and used dry ice everyday for delivering some perishables like icecream. I would reuse the dry ice in the warm weather for my lunch. So, I'm kind of an expert. LOL.