Phil, the hose from the outside shower would work well -- the only problem is that you would have to go outside to turn it on. We did somehow keep the trailer at about 32 at night -- I think it is such a small trailer that our body heat was enough. We did not run the furnace after bedtime -- too noisy. A catalytic heater is an option, but we are ok without it, I think.
And I did not know that I need to keep the camera above freezing -- it seemed to work fine in 15 degree weather at night. It has a rechargeable lithium ion battery that lasted us the whole week without recharging.