I have two portable ac/dc fridge/freezers,and Engel(most efficient) and an Iceco..They easily run for a week on a 100ah LP battery in refer mode..One 100 watt panel keeps one,charged..Right now I am experimenting with one in freezer moder(0 degrees) and one in refer mode(32 degree's) with one 100 watt panel..On a sunny day it barely keeps up replacing used AH,on cloudy days usually two 100 watt panels are needed and sometimes it takes three 100 watt panels to do so..But it does and two of my 100 watt panels are portable..
I am at 20% this morning on my primary battery with a cloudy day forecasted..Rather than mess with portable panels I will just hook up my 10 amp Norco charger to get it back abone 50%..
So yes you can run a DC refer off of solar if you choose one that is easy on the power,not a power monger..The 10cf I saw use about 84 ah a day,that is way to much for me and my setup needing maybe 400 watts of solar at a minimum..