Sounds like I need to do some research on portable solar arrays. Then I plug into inverter, then battery? It's hard to get a sense of how it ties together from my google searches.
If you have a battery involved, you should not be using it to run the fridge at night anyway, but most inverters expect to see a battery, so you might need it. In such case; solar array to charge controller, charge controller to battery, battery to inverter, inverter to fridge. There are better ways to do this, but this is the most simple I can think of.
But also consider Regulator's suggestion. If you don't need the fridge ongoing, you likely don't need more solar than you need to charge up your cell phone or shortwave radio in a couple hours. Ocean going sailors have been doing this one for centuries, and there are plenty of tricks. One that I'm testing out currently is bean sprouting. A 5 lbs bag of beans in a tupperware tub can last a long time, and are good both in soups and stews as they are, and sprouted on a salad. It's a different food after they have been sprouted for 4 or 5 days, with a different nutritional spectrum. Canned goods are okay, but don't buy any that you wouldn't eat anyway. Truly cured meats are expensive compared to their refrigerated versions, but can be kept on the shelf for months. You can get canned butter & canned meats from Amazon, but again, more expensive than their refrigerated versions. But butter doesn't really need to be refrigerated, just kept away from oxygen if on the counter, which is what a butter crock does. I have a one stick butter crock, that looks just like a bell upside down inside a cup of water. Butter can last for a month that way, if you change out the water every three days. Don't try this with margarine, though. Almost every condiment that Americans keep in the refrigerator don't really need to be, except mayo. Hard cheeses, like butter, only need to be kept away from oxygen; and you can literally take a block of cheddar from the store and seal it into cheese wax for a year.
