Driving around with lights on probably draws 10-20 amps. Stereo draws another 5-10 unless you go crazy (which would be stupid, given it's a noisy Land Cruiser.) The ignition itself draws little power. These are quesstimates, but close enough, the point is that there is plenty of capacity for your needs.
Most batteries are 50-75 amp hours. So if your 4.7 amp fridge ran continuously (which it won't), it could run at least 10 hours on a 50 amp hour battery. The reality is more than twice that long. I am careful not to park in full sun, which decreases the cooling needs substantially. What fridge do you have? Most ARBs draw 2.7 when running except the 60 quart model.
Just as a real world example. I have left the fridge running in Rubicon springs for 3 days, and still had enough juice to start the truck. I'm careful about opening it only when needed.
If your intent is to run a fridge, I might suggest a deep cycle battery. Standard car batteries do not like big discharge cycles.