I'm gonna weigh in with JH and also say no on the 12" gas logs.
Standalone gas log sets are intended for use in a fireplace that has a good draft to remove carbon monoxide, as well as the large volume of fresh air of a house, not to mention some constant source of fresh air.
Wood/coal stoves, including marine versions, are generally not rated for use with just any old set of propane logs. Stove manufacturers have gas-burning stove setups specifically for that purpose.
I wouldn't recommend even the unvented gas fireplaces and stoves rated for mobile home use because of the much smaller volume of a travel trailer.
There are vented marine gas stoves suitable for use in a travel trailer. Some examples are posted in the forums here.
We keep our Airstream winterized year round, and bring water and a porta-potty aboard, and don't use the sink drains when we want to use it. Even with a vented marine gas stove, but without forced air heating ducted below the floor to keep your tanks and plumbing freezing, I strongly suggest you do the same.
Depending on where you are and how cold it gets, even WITH forced air heating ducted below the floor, you may need to skirt the trailer to eliminate the effect of wind chill, which removes heat faster from the underbelly than stationary cold air. Without this, even the ducted hot air may not be able to keep up with the heat loss.
Even with a vented stove or RV furnace that vents the products of combustion (one of which is water) outdoors, humidity from your breath, bathing, cooking and washing dishes can be a serious problem in the small volume of an RV. The condensation that results from it can cause damage inside the unit. Besides having a dehumidifier, the main way to fight that is by venting the hot, humid air at one end of the RV and introducing cold, dry fresh air at the other. That's also a good thing if you like to breath, but it adds to your heating load.
Just some thoughts... hope they help.