Hi, Sara! Fitting that I should see this thread, as I too will be living in a Prius soon, and have been pondering the EXACT same things you have...even just today :thumbsup:
Most of the portable fridges I've researched (Alpicool, Iceco, Costway, etc.) all pull around 40-50 watts. If you used something like a Jackery - especially the higher wattage ones - you can run the fridge continuously for days on end...provided you really aren't charging other items at the same time. But here's where it gets even better...
If you connect the Jackery to a 100 or 150 watt solar panel, that should be more than enough to top-off/replenish the Jackery as its charge decreases. Obviously, there are a LOT of other variables involved, like; sun angle, strength of the sun, etc., so do keep that in mind. However, I've seen MANY videos of others with similar set-ups, and they all run their fridges continuously without any issues.
Take a look at this gentleman, who is very informative. He did a breakdown on how long each of the Jackery models could power a fridge:
As for the sizing matter, I'm EXACTLY where you are on this now. I was looking at the 50 quart Alpicool today, and it is VERY tall. Like you, I'd rather not having it under the seat. So, my thinking is that it would go next to my twin mattress where the rear hatch opens. But after considering the size, I'm not sure how much headroom/clearance I'd have to lift the top open. Especially since I haven't purchased my Prius yet...it's mighty tough sizing everything without the actual car!
Just curious...have you purchased your Prius yet? Maybe we can lean on each other and share our research regarding things, since we're both at about the same stage of this process.
Anywho, I'll definitely be watching this thread closely. Good luck!