I am going to install a hitch for the 2008 Honda Pilot. Will it also need transmission cooler?

 

You should not need a an additional cooler just remember to take it out of overdrive when you take off while pulling a trailer,this saves the stress on the Trans.

 

Depends on what you are towing. Occasional small trailer around town. Probably not. A boat? Probably yes.
They are cheap and not hard to install. Inexpensive piece of mind. I’d skip the recommended power steering cooler.