I'm no expert here, but since the furnace - whether regular type or hydronic - must work when dry-camping and therefore on 12v, your thermostat should be 12v as well. The air conditioner units themselves obviously run on 110v, but that doesn't mean the thermostats that control them have to be 110v. That's what solenoids are for.
Recent threads here re. owners replacing older roof airs have broached the problem that not all thermostat controls mesh 100% with the latest available models, and vice versa. Hopefully some of them will provide insight for you. You could also contact the manufacturer of your A/C - Dometic DuoTherm, Penguin, Coleman - for advice.
Joel