Need a special tool to remove oil cooler

I'm assuming this is a 4.0L V6 - as you did not mention which engine you have. According to the shop manual instruction, It merely states to "loosen the threaded insert". There is no special service tools indicated in the Ford shop manual, which would absolutely be listed if the tool was somehow special. Sitting here at my computer and not under your Mountaineer, I cannot describe which tool you need, but I'm fairly certain it is a wrench of some sort that most auto technicians would have in their "standard" box of tools. I would suggest taking a photo of the "threaded insert" and taking it to a local shop near you to get some direction.

Allen drive fasteners (bolts) have six sided (female) heads - which would resemble the head of a bolt. Google > Allen drive bit socket - now that doesn’t give you the correct size you’ll need - it is just for reference purposes.. You will have to to the rest. Good luck!