The OP asked about 'rough terrain', and 'rough roads'......there IS a difference, because dirt roads, forest roads, etc are technically on a road.
'Off-road' or 'rough terrain, means (to most of us) not on any kind of 'road'. Cutting your own path thru rocks and brush and gulleys and deep sand. THAT'S 'off-road'...and usually rough terrain is a part of that. I seriously doubt the OP will try that with any kind of travel trailer.
ATV trails...well some of those are on a 'road'...and some of them are thru some really gnarly terrain...and I dont think the OP intends to try any of those either, with a travel trailer.
I think we can assume the OP means: dirt roads with the occasional dips, potholes, and ruts, maybe some loose sand and gravel in places. Might even pull off the traveled portion of the dirt road to get a good spot...
And yes, some smaller travel trailers (and pop-up trailers) will handle some of that, occasionally. It depends on the tow vehicle and of course the ground clearance that the trailer has available, along with some other factors, including tires, suspension travel, modifications to the trailer hitch and drawbar/tongue, ability to self-extract or self-recover if traveling alone, etc etc.
I dragged my little r-pod trailer off-road last year, YES...OFF ROAD, and neither myself nor the trailer liked it...we wont do THAT again!