Running your beer fridge off the car's starting battery is a really, really bad idea.
A small car starting battery has a capacity of about 50 to 80 Ah (that's 4A for 12.5h to 20h to completely kill the battery). You wouldn't be able to start the engine with more than 1/3 to 1/2 of that capacity gone.
Running the engine (say a couple of times a day) to recharge the battery is not realistic, either. At best, the car's charging system charges the battery at about 35A, provided that the engine runs at ~1500 rpm, so you would have to start the car and run it for an hour about twice a day just to replenish the charge and still be able to start the car the next time.
A large deep-cycle storage battery is expensive, and heavy. One of those, fully-charged, still only has a capacity of ~120Ah, so that will not do it.
I have gone on backcountry river trips (including running the Grand Canyon) that lasted 8days. The only way we could keep meat frozen until the six/seventh day was a very large ice chest (cooler) solidly packed with frozen food surrounded by dry-ice. You had to minimize the number of times you open the lid to less than twice per day, so this was not used to cool drinks. This ice chest was huge. It would take up the entire back seat of your Fiesta and it took two men to carry it...
There are two energy sources that are routinely used in the Recreational Vehicle Industry for this purpose, and duration. One is gasoline (to run a generator), and the other is propane or LPG (to run a gas fridge). Batteries do not even figure into this equation.