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Water heaters ... Yeah, they're like the instant inline-heaters you can get for your house. The cold-weather package insulates the tanks and may throw some heat tape around them.
There's generally two energy sources things run off of: 12V DC and Propane. Most people opt for a generator to run 120v appliances and charge the 12v house batteries.
Lights, furnace blower, stereo are 12v.
Furnace and stove are probably going to be propane.
AC and microwave will connect to the generator.
On the topic of generators... 1kW is good for minimalist camping. It's plenty of power to charge the 12v system and run small items.
I have a 2kW, which is good for what I need. I can hook up my battery charger (12v/15A, about 200w at full output), 600w halogen work light, charge my computer/camera/phone/radio batteries (probably 150w combined) and still have power to spare. Since it's 2kW output, I can run my 1.2kW microwave off it, which I couldn't do with a smaller genset.
AC units require a -lot- of power. Even with the small ones, you're going to be best off with a 3kW or more generator.
Get the inverter models, they can adjust the RPMs to maximize efficiency if you're not putting it under heavy load. The 5kW+ construction generators run at a constant 3600 RPM... they're loud and suck a lot of fuel if you're not using the wattage.
Pic related, my setup. Generac iX2000 genset by the front tire, 40lb propane cylinder by the trailer. Furnace (intake/exhaust are top-rear on the side of the trailer) runs off propane, and the generator kept everything powered/charged.
On the house battery, I can run for a night or two (depending on how often the furnace is running) without running the generator, which is nice.
