A portable Fridge Freezer would work for your needs. They come in many different sizes. They are more efficient than a fridge with a side opening door as cold air does not "fall" out of the door when you open it. They have top opening access doors.
You can take them indoors in the off season for storage if you wish to. You can also take them along for car travel without the trailer. There are mounting plates available for securing them in place.
Look for one with a "Secop" compressor, also historically known as "Danfoss". Those are very reliable compressors with good energy efficiency. The company was Danfoss has been going through ownership and name changes since 2010. https://www.secop.com/about-us/who-we-are/
The Engel units are also excellent and efficient in terms of energy use but they take longer to cool down than the Secop compressors which can be an issue with last minute travel decisions.
These types of AC/DC fridge freezers will run nicely off of solar power
stored in a battery and they have protection built into them to prevent over draining your batteries.
Lots of good brands of the portable fridge/freezers around. Be sure you pay attention and do not purchase a portable cooler that is not rated for freezing temperatures as it won't reliably keep your food cold enough for safety. Avoid units that state they are a cooler and warmer, those are the wrong kind to buy. Do not buy a wine cooler, they are also not cold enough.