Heating the trailer in the winter

No different then heating it up when using trailer.

If you have working 12V DC and propane..run the furnace

Course if battery is only source for the 12V DC then will need recharged long before running out of propane

Rule of thumb (sorta)....1 battery/1 night of furnace

The only real issue is when you do electrical then perhaps no 12v for furnace and when you do LP then no gas for the furnace. I suggest a nice heavy duty extension cord to the rig powering a ceramic heater when furnace cant be used. They can warm a rig fairly well and in this case keeping your tanks warm is not an issue.

As long as the trailer isn't in an enclosed storage space so you have proper ventilation, running the furnace should not be a problem. That's what the furnace is for, warming up the interior for when you are in there.

do it quite often when doing repairs in the winter, likewise using AC in the summer. As long as the trailer isn't in an enclosed space your ok. And don't have the trailer such that the furnace exhaust would vent into or very near your house either.

Don't want any CO issues.

I like to put the trailer in the driveway and plug it in to work on it. Then there is power, lights, and juice for the heater or A/C. Tools are close by. Open the vent a crack a window.

OP here.
Trailer is parked on some planks on my lawn so it does not sink into the ground. I leave it uncovered. It is close to the house so I can easily run hydro to it to run lights and charge the battery. I even have a second battery that I could hook up if needed.

The work for the propane is to remove the regulator for the Hot Water tank and to replace the stove.

The Electrical is to replace the Power inverter, tank level indicator, and light fixture.

I would turn the furnace on the night before and then turn it off when I start working on everything.

Mine stays outside and plugged in to keep the battery charged and for any mods I want to make. I use a small ceramic 110v heater (I also use it when camping too instead of the furnace) warms the unit up quickly.

The furnace is there to heat the trailer when it's cold in it.

I also use a small 110v ceramic heater as described in several replies above. I use it to heat the TT when at home and I'm working or cleaning inside and save the LP for when we're on the road.

We prefer a small ceramic electric heater over propane all the time. We rarely fire up the furnace when camping.

Propane works well and can heat the TT very fast but an electric heater provides a clean heat source, generally suitable for a work environment.