An alternative to pet management may be to keep them in their own enclosed spaces. That could be as simple as a carrier with a blanket over it or a section of the dinette with cushions used for walls. That would allow you to turn the heat down and less condensation inside.
FWIW, I've built a number of pet houses and a cat or dog (the more hardy ones) can endure very low temperatures as long as they are enclosed, away from wind, and can use their body heat to maintain/raise the temp of the enclosure. Your storage area with no doors sounds like a good area for pet housing. Cut some holes and cover with what you like. I have all my cabinet doors and accessory spaces covered with a durable outdoor woven nylon. It allows a small amount of air transfer.
In any event, using a furnace in a small box means that you will need to provide ventilation. I have a trailer similar in size and I built it with vapor barrier and thermal breaks to any outside surface. I have Low-E, multi pane windows. I still get a small bit of condensation on the glass so I keep a vent and/or a window cracked if camping for any length of time in the Winter.