Some aren't too bad. Sundanzers are designed to run on fairly small solar setup. They're pricey though.honestly the refig would suck more juice than it would be worth unless you have alot of pannels id use for radio and other things if i am living on solar ima be using my root cellar
But for conventional fridges a small dorm fridge isn't too terribly bad but still takes a ton of panels. The one we have draws 10amp per hour at 12v. That's alot of juice to replace in only a few hours a day.
Even a small microwave would suck major amounts of power from your batteries. Only good thing about it is that they only run for seconds to minutes at a time. A 1000 watt microwave draws roughly 10ah @ 110v or 100ah at 12v (these are rough numbers). With conversion loss that equates to about 2 amps per minute.I am going to put in a microwave to heat meals so I dont have to use my propane stove except on a rare occasion.
Not saying it can't or shouldn't be done but you need to keep the numbers in mind.