To the original question re: Electric heaters, I'm a big fan of the oil filled units. But you cannot run one of those from a battery, it will drain it quickly. They are also bulkier / heavier than the small ceramic style heaters.
For camping without power I won't use anything that has an open flame inside the trailer (like a Mr. Buddy). I know lots of people who use them, and most of them are alive to tell you about it, and yes, they can be used safely when there is good exchange of outside air but inside of a well sealed trailer is not safe. I have seen firsthand what happens if they are not used properly in a 23 foot trailer with 6 people. One survived the CO poisoning, 5 didn't. The Mr. Buddy does include a "Oxygen Depletion Sensor (ODS) and accidental tip-over safety shut-off" to make it safer than the other types of propane heaters that don't. But the fact that it needs an Oxygen Depletion Sensor means it can be a problem under certain circumstances.
The furnace in your trailer is a heat exchange style unit, flame venting outside heating tubes with flowing air on the inside. That generates no carbon monoxide inside the trailer. They have wall mount versions that you can add to your garage, you just have to cut a couple of holes in the wall to allow it access to outside air and get it propane. Sounds like a big deal but the walls are already cut up pretty good with windows, hatches, doors, appliances...
Just my opinion, and yes, I have kids, and yes, that impacts my comments on this post. Single guys in trailers can do whatever they want.