Connecting Generator to Trailer

The other problem as StephenH says will be keeping the furnace lit as you boil off propane and the cylinder liquid temperature drops due to boiling off the propane. It takes about 700 btu to vaporize 1 gallon of propane and our 20000 btu/hr furnaces will burn about a gallon every 4-5 hours so they will need about 150 btu/hr of heat delivered to the cylinder to maintain its temperature. That's not a lot but some way of transferring heat to the propane is required.  This is where a larger tank helps because its larger surface area absorbs more heat from the environment than a smaller one. Placing the cylinder in a warm location will also help, or just placing it in a water bath. 

We heat my wife's studio with propane and the tank is outside in the cold.  We've had no trouble lighting the heater even when the temps are down in the single digits.  StephenH, how can you say that there isn't phlogiston in propane?  

Quite frankly, if it's too cold for the propane tank to supply gas, it's not likely that one would be out camping in a marginally insulated rPod.  You'd be going through a tank of LP every day or two just to keep warm.

This is a handy chart to compare the relative amounts of energy per unit of various fuels.

Phlogiston has nothing to do with it. BTUs per gallon does. LP does burn cleaner than gasoline, only because it is a single type of molecule instead of the blend of molecules that is gasoline, some of which burn cleaner than others. The down side is that it takes more gallons of LP to get the same energy output.

Here is one example I found of the relative power output of a generator on gasoline vs. propane:

3800 running watts/4750 starting watts (gasoline)

3420 running watts/4275 starting watts (LPG)

Edit: I found a chart for a Champion dual-fuel inverter generator. The comparison is:

Gasoline:  3400 starting and 3100 running watts

Propane:   3060 starting and 2790 running watts

Also, most of the sources I saw stated that in temperatures below 20F, the propane was not viable unless there were a method of warming the tank. Even below 40F, the pressure in the tank starts to drop and may become too low to start the generator on LP alone. Even though the boiling point of LP is -44F, as the LP is used out of the tank, it cools the tank to below ambient temperatures. It isn't unusual to see frost build-up on the tank when LP gas is used at a high rate. With ambient temperatures in the teens or single-digits, it may not be possible to maintain sufficient gas flow to run the generator, especially if the same tank is being used to supply the furnace. A separate tank would be better, especially since it could be placed in the area where the cooling air for the generator is exhausted which would warm the tank. However, it would be prudent to not place it in the exhaust from the muffler so that it does not become overheated and start to vent propane from too much pressure.