Theo, the trailer burning down kinda speaks for itself, doesn't it? Yes, I longed for the warmth of the photos at the marinestove.com website when I first saw it. A woodstove would probably play havoc with your smoke & CO detectors. There probably isn't much safety margin with the low internal volume of a trailer.
The trailer's furnace usually has a function of forcing heated air around the water tanks, delaying freeze-up. Accessory heat of any type prevents that from occurring. An outside fire ring provides the coziness one could want -- at least in weather most of us accept for trailering.
If you're still "crazy to.." take a look at
West Marine and do a search on the word
heater. Select the 'ventilation' results and browse away. There's wood, there's LP, there's diesel (egads!). Putting stovepipe through the roof would be quite the custom project. Remember the rule-of-thumb about the chimney reaching three feet above any other structure within ten feet... Now I want to see that traveling down the road!
I think seasoned firewood for the fire ring would easily fit within your truck's capacity.