The fridge will be an issue; it an absorption fridge (ammonia) and doesn't like freezing weather.  Make sure to insulate the vents and leave just a small hole (1/3 of a louvre) at the top.  If its regularly below freezing, you'll have to put a 60 watt incandescent bulb back there as well to provide heat.

Your tanks will definitely be an issue.  Definitely skirt.  If it snows, pile the snow up against the skirt for better insulation.  You may end up having to put a 100 watt incandescent bulb under there.

You valves will freeze.  Expect it.  Wrap 'em in heat tape.

Your fresh water hose and sewage hose will freeze.  Keep the fresh water hose in the trailer, take it outside only to connect to the tap and fill your fresh tank.  Then, disconnect it and bring it back inside.  Ideally, you'd do the same with the sewage hose, but that'd reek.  Instead, leave it connected.  Make sure there are no dips where water can collect (use a slinky stand).  Do not leave your valves open - only open them to dump and then close them again.

And, of course, run fridge and hot water on electric only.  Propane, insulation, exhaust gas, and living people do not mix well.  Tape down the propane switches and mark them clearly as DO NOT USE just in case someone other than you thinks that using propane might be a good idea.

Oh - put a layer of reflectex under the bed and behind the dinette cushions.  After a few very cold nights, you may also want to consider putting a layer around the bed and up the bedroom walls about 3'.   An electric blanket is also an excellent idea.  And a night cap (both of the wooly and alcoholic types).

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To be honest, unless you're very hearty and feeling adventurous, I'd suggest finding an alternate arrangement.  Wintering in an r-pod is going to be tough at times.  A long-term stay at a cheap hotel, cooking on a 2-burner cooktop may not sound like a great idea... but its not *that* bad.