Adding salt lowers the temperature and makes everything colder. But it won't make the ice last longer. Colder temperature in the cooler means a higher differential temperature to the outside and faster heat transfer to the inside.
I've never done it and wouldn't bother, but you could probably make ice last longer by covering everything in the cooler with a few inches of Ping-Pong balls. That would add a floating layer of insulation that's still pretty easy to reach (if not see) through. A few layers of big packing bubble would work too.