I came across this awhile back. Some people were taking a chest freezer and running it like a fridge. It makes sense too. Cold air is heavier than warm air, so when you open up a regular fridge, then the cold air "falls" out to the ground. But in a chest freezer or fridge that doesn't happen, the cold air is trapped. That makes the chest freezer or fridge incredibly more efficient for its size than a stand up type.
The simple way to do it is to take a freezer and put an external thermometer nearby. The probe will go inside the freezer and sense when to turn it off or on. The power for the freezer goes through the external thermometer and literally turns the power off or on, just like plugging it in or unplugging it when it needs to. Here is what that device looks like.
This is what that thermometer looks like and here is a closer look.
A typical fridge may use 1.8 kwh per day or 1800 watt hours per day. Solar powered at 5 hours of effective full power sun a day would mean 1800/5 = 360 watts of solar panels or about $2500 just to run the fridge. Some examples with running a freezer like a fridge shows roughly 100 to 300 watt hours per day for about 16 cubic feet. So, worse case, 300/5 = 60 watt solar panel or about $400 instead of $2500. They make $2000 Sun Frost fridges meant for solar power, but this method is as low power as theirs and you can do it with a $200 freezer, not a $2,000 device. You can find this device here but you might could find it cheaper elsewhere as well.