I would question why anyone would refrain from installing a transmission oil cooler for any tow vehicle equipped with an automatic transmission if it does not already have one. Pulling any type of trailer is adding weight to the tow vehicles drive train. The transmission is going to work harder, along whith the rear end, and engine.
It amazes me how folks will change their engine oil more frequently (this is good), but will neglect to have the automatic transmission fluid flushed every 30K, along with its pan dropped, and a new filter. The rear differential oil should also be changed every 30K.
2015 Jayco Jay Featherlight SLX16XRB (TT)
2007 Ford F150 Tow Vehicle (TV)