The ice trade only became viable on an industrial scale by the nineteenth century, but Ice Houses for storing ice long enough to last the year have existed for well over three thousand years. sawdust and straw are decent insulators, and the square-cube law indicates that for eight times a given amount of ice, you'd only need to double the insulation, so it scales up pretty well (well there are other factors that would make building a larger ice house difficult, not to mention logistical concerns).
Chemically, Saltpeter's been used as a coolant since the Romans, just add water. want to recycle? boil it off. A similar salt, ammonium nitrate, is the primary ingredient in instant cold packs (the other one being water).
My point is that ice would probably be expensive anywhere powered refrigeration doesn't exist, but that it shouldn't be unheard of.