You have to switch the gas off on the shorter crossings, certainly - no experience of a longer crossing - but some 'keeping food cold' tips:
1. Buy a good quality coolbag.
2. Put it in the freezer. You may have to 'eat up' some freezer contents to make room.
3. Freeze everything you want to take, plus some litre cartons of orange juice, etc. Put the cartons of frozen orange juice in the fridge to really cool everything down.
4. Pack everything else in the cool bag, as tightly as possible, and fill any space with folder tea towels or similar, and put in a cool place in the caravan.
5. Run everything on gas or 12v whilst travelling, and only switch off when you absolutely have to on the ferry!
We've found, doing this, keeps everything frozen or semi-frozen for at least 36 hours - and even then things are colder than fridge temperatures. We've been doing this for 17 years, caravanning, without any problems.