I see a number of options here and as several have pointed out, a large percentage of the world's population lives without refrigeration, so the issue is not whether one can live without a refrigerator, so it boils down to resources and choices. If you want refrigeration, I assume the issue is how much money and/or effort you want to spend. There are obviously off-grid refrigerators, but if you don't have (or don't choose) to spend the money for one of these options, then one can also spend a lot less money and still have some refrigeration/ice. For instance, if one has PVs, one can super-insulate a cooler and use an inexpensive ice maker when there is sun. Ice can simply be seen as a type of battery that stores the cool for night (or longer depending on insulation and amount of ice made, etc)
