Overcooling a tranny is pretty difficult to do. About the only time it can be a problem is if the fluid is too viscous that it won't flow properly. If it's too thick, the pump can have a hard time moving it.
That being said, usually that has less to do with overcooling and more to do with not having the proper fluid.
With a trailer that size, an aftermarket cooler would definitely be a wise investment. Heat is a transmission's worst enemy. Keep a transmission at an appropriate temperature, the fluid stays healthy, and that leads to the guts lasting longer. Overheating the fluid results in a breakdown and deterioration in the fluid which leads to a rebuild or replace situation.