Hi Scotty,
This summer I’ll be towing a 4x8 enclosed uhaul trailer with my 2012 Impreza (manual transmission).
The trip is a little over 1000km (620 miles).

Will I need an external transmission cooler for this trip?

Manual trannys don't need that, they are just splash lubrication. Only automatics need that

Well I learned something today!
Thanks so much!