Trailers do not have a GVWR.
Maybe not the little trailers. But any trailer that can handle carrying a skidsteer certainly does.
The Hudson trailer I use has a GVWR of 18,000 lbs. and a GVW of nearly 5,000 lbs. The F550 power stroke that pulls it only requires a chaufers license (as a comercial vehicle), but to tow the trailer (even empty) you need a class A CDL (yea, the same that is needed to drive the biggest semi) The only difference is that an air brake endorsement isn't needed, since it has electric brakes.