Horse size Road Cart on trailer roof, would also likely be too tall for bridges and overpasses with the bigger wood wheels. Most have between 40 to 54 inch tall wheels, plus cart body is high enough to see over horse, look ahead when hitched.
Saddlebred, Morgan, Arab, Western breeds use carts with smaller wheels with tires, single person, low seating on the body. So those type carts, very light weight as pictured in Red Mares photo, can fit on trailer top with few issues.
There are some welders who have created an extra gate frame, using trailer back door hinges to hang it from. Gate is outside the trailer, behind rear door/ramps. Cart is supported on the gate, fastened in place, shafts up, for hauling. Gates I have seen photos of had smaller wooden Meadowbrook or Road Carts, used with Arabs, big ponies or minis.
Not seen any big Road Carts like used with draft horses on a back gate. Those big carts have long shafts, 84-96 inches plus cart body for a full length, along with the big wood wheels, 54-56 inches tall. Those long shafts might catch a lower bridge or walkway! Lot of weight too, for lifting and hanging it on the gate frame. We back the big cart into rear of stock trailer, block and tie it down, close the back door with shafts sticking out above the locked rear door for hauling. Tie the padded shafts down from the outside.