Replace transmission cooler???

[Hammerhead]

First things first! If you can SEE coolant leaking, you are unlikely to have a tranny cooler issue. The vast majority of tranny cooler leaks leak coolant INTO the transmission, not externally.
If you do have a tranny cooler leak, ASAP after R&R'ing said cooler change your tranny oil. Coolant contamination of tranny oil is guaranteed to cause your rear synchro to fail. Yes, that's experience talking!

A Pete is one of the easiest trucks to R&R a tranny cooler on as when you pull the shifter plate off the floor you have the biggest opening of any truck...except a COE.
I'm too far away to come help you do it, so I'll tell you...
Tools required:
2 pair of vise grips; to clamp the coolant hoses shut if you don't want to or have the equipment to drain your coolant...or
3 @ 5 gallon buckets to hold your coolant
Large wrench set, or 2 large crescent wrenches to R&R the oil line hoses. If I recall correctly it is a 1-1/16 & a 1-1/8. You can verify this first by checking the hose fittings on the lower right front corner of the tranny. They are almost alway the same size as the top ones...unless you have to get new hoses made ASAP at a small farm dealership like I did and he didn't have 4 the same brand, don't ask!
Small wrenches to unbolt and replace the cooler
Pliers, or small wrench or socket to undo the coolant clamps; depending spring or screw type.
One skinny bastard! I'm about 5lbs smaller than Rawze and this job is a royal PITA on my T800, but that big hole in the floor of a Pete makes this requirement more of a perk.
Some spare coolant to replace any lost coolant.
Teflon tape or goop

Job details:
Drain coolant into buckets, or clamp off the coolant lines. If clamping, I suggest resisting the urge to clamp close to the cooler to minimize loss. If you bump a clamp the wrong way, your going to lose a significant quantity, so bit the bullet and clamp near the head and the return line. I know, it sucks.
Remove shifter plate from floor of cab. Preferred to also remove shifter and lay it down on the floor. Removing air lines not necessary this way.
Through the shifter hole;
Remove coolant clamps and hoses from fittings.
Remove oil lines from fittings
Then unbolt the cooler from top of tranny.
Remove cooler, transfer all required fittings using Teflon tape to prevent leaks to new cooler,
Reassemble in reverse order...

Would I do it in a parking lot, yes. But I've also changed a front diff in a parking lot. I carry wheel nut sockets and replace wheel seals, tires, fix flats, etc. myself on the road.
If it's your first time, and you brave it and do it yourself...I'll buy the first round when we meet and let you tell the story!
Expect about 4hrs flat rate for a shop. Like I said a Pete is about the easiest there is to do it on, but good luck getting a shop to pass in the "easy button" savings...

I'd expect if you have all the tools and are handy, it will take you about 4hrs or so...
Good luck, and let us know how you make out