Also a nice thing to keep in mind when buying a solar panel is the watt rating and how it’s arrived at. They get the rating by putting the panel in the sun on the brightest of sunny days. Under normal conditions you will get clouds & some shade. This can and will cut the panels output in half or more. So a 50 watt panel becomes only 25 watts for 30% of the time you are trying to get power out of it. The best way to make good use of a solar panel is to have it as part of a 12-volt (or 24 or 48 volt) system. For a DC system you need a battery, solar panel, charge controller, possibility an inverter, larger wiring as DC voltage requires heaver wires with the same voltage then AC does. And a lot of other small things to make it work. Most of these things can be made easily from parts from other things. But the one big expense is the solar panel.

So, you can't get there from here? Meaning there is no small solar powered car cooler that actually works well off a reasonable solar power source?

Don't use solar power - It causes global warming. It also will make the sun burn out faster.

Compare a chunk of ice to one of those thermoelectic coolers. The TE device will use about 50 watts to produce about 15 watts of cooling. One kg of ice will provide the same rate of cooling for six hours. A 1 kg gel cell battery will run the cooler for about a half an hour.