Should I get a 12V cooler instead of a passive one?

Yes, if you want zero ice. A passive cooler needs ice or gel packs to work; without them, food spoils fast. A thermoelectric 12V cooler keeps things cool but not cold in heat. A compressor cooler (like Dometic or ARB) freezes food and uses less battery but costs $500+. For no ice at all, get a proper 12V fridge.