As long as you are monitoring the trailer OFTEN, there should be no problems doing this. However, I suggest a backup electric cube heater set to a lower temp than the main thermostat, to act as a failsafe in case the propane tanks run dry or the furnace fails to light.
If the trailer is close by your residence, you can install a remote thermometer and keep an eye on the interior temp from your house.
I think going away and leaving your trailer at a remote location while relying on the just furnace to keep it from freezing is a HUGE, possibly expensive mistake. RV systems are simply not as reliable as residential units.
BTW, if you park your Ollie beside your home, can you run a propane hose from your big propane tank to the trailer, using a quick disconnect fitting, so you don't have to worry about the little tanks running dry? That would be a neat mod, as long as you remember to disconnect it before leaving!
John Davies
Spokane WA