There are 2 kinds of Cat heaters. Vented and non-vented.
The vented style have an itty bitty 12 VDC fan that will exhaust the bad gasses to the exterior of the trailer and you do not need to have a window open.
The non vented have no 12 volt
draw, but to be safe you need to have a vent or window cracked open to allow the bad gases to exit.
If the unit is a vented one, I say add a vent and hook up the fan. The fan will create a slight suction and you will have fresh air drawn into the trailer from many little openings.
The draw of the fan is no where near what it takes to run a furnace so you will not be killing your batteries to run it.