Watch the humidity in them. .More than just your breath, cooking with propane, and heating with propane cause more moisture in the travel trailer. In humid Oregon, this translates to taking an inch of water out of the windows daily. I would highly recommend a dehumidifier if you can afford the power (electric vs battery vs generator vs solar), keeping to vents/doors/windows opened or cracked as much as possible. Keeping cupboards open as much as possible.
Watch anything which comes in contact with walls, such as your mattress at the top of the bed, pillows. They will pick up condensation and mildew. We now keep our clothes in duffle bags on the main floor, as we got fired of damp clothing all the time. We do not have a run down trailer either, I will post a pic when I can, but humidity is humidity. Something many people don't consider.
We cannot use a dehumidifier, due to power consumption (also check and see if your breaker box will support it), but we use alot of those dri-z-air tubs. And tend to dump them daily most days.
Showers I try to open vents and doors.