The short answer
RV heating comes in three families: a propane furnace that warms the cabin air directly, a hydronic boiler that heats water and a separate loop of radiators or floor piping, and a diesel-fired heater that burns the vehicle's own fuel to make hot air or hot water. Cooling is either engine-driven, run only while you drive, or mains-driven, and that distinction is why an RV in a hot climate is often cooler in its cab than in its cabin.
Furnace: cheap, simple, thirsty
A propane furnace is the standard solution and works without any engine or mains: it takes air from the cabin, warms it and returns it, usually with a ducted or a blown-air layout. The cost is gas. A well-insulated European campervan at 0 degrees outside will burn roughly one to two kilos of propane an hour while the furnace runs, which empties a small bottle in a day.Budget a second bottle and a spare. It also needs ventilation and a carbon monoxide alarm, and the return air must not be drawing from a sealed cupboard.
Boiler and hydronic heat
A boiler heats water, and the water heats the cabin through radiators or through piping embedded in the floor. It is slower to respond but far more comfortable, because it radiates rather than blows, and the floor loop keeps the whole cabin even at a low temperature. It is the system most commonly found in European motorhomes and is usually plumbed into the same loop as the hot water. The catch is water: the boiler holds water, so it must be drained or antifreezed before a freeze, and an empty boiler fires on a dry system.
Diesel-fired heaters
A diesel heater burns the vehicle's own diesel to produce hot air or hot water, and is the reason a truck camper or an expedition rig can sit in the snow with the engine off. It needs a fuel line, an exhaust for the combustion byproducts and a professional installation to be safe; a badly installed diesel heater is a carbon monoxide hazard, not a comfort feature. It is quieter than a generator and needs no propane, and it is the preferred solution for anyone who sleeps in the vehicle every night in a cold climate.
Air conditioning
Engine-driven air conditioning only works when the engine runs, which makes it useless on a static pitch. Mains-driven units run from a 120 or 230 volt hookup and are what you use while parked. A generator or a large lithium bank plus an inverter can run one, but realistically you need the hookup or a big generator. In a hot European climate parks are often chosen for their shade first, and cross-ventilation plus two good vents beats any single air conditioner for comfort.