So just slap a power inverter in there somewhere and you're good to go
To answer the original question, a fridge requires quite a lot of power to operate. Could be 500W. There's also power loss from the voltage conversion, so you need a battery and an inverter that are able to provide more than that - let's say 600W. Car batteries are typically 12V lead-acid batteries. 600W means 50 amps from the battery. That's a huge current. Lead-acid batteries can handle high currents for a short period of time, but high currents have a negative effect on the battery capacity. So my guess is that the fridge could work for a very short period of time.
So just slap a power inverter in there somewhere and you're good to go
To answer the original question, a fridge requires quite a lot of power to operate. Could be 500W. There's also power loss from the voltage conversion, so you need a battery and an inverter that are able to provide more than that - let's say 600W. Car batteries are typically 12V lead-acid batteries. 600W means 50 amps from the battery. That's a huge current. Lead-acid batteries can handle high currents for a short period of time, but high currents have a negative effect on the battery capacity. So my guess is that the fridge could work for a very short period of time.
Probably lost about 10% or more to heat.
10% worse efficiency > no refrigerator
Maybe refrigerator until the battery catches on fire!
Inverters have gotten pretty efficient. I have one for my house that's 97.1% efficient.