Here's what I was told when I ran it by my local club:
"The tranny cooler integral with his radiator. it uses the engine coolant to 'cool' the tranny fluid. This works for OEM vehicles because the tranny will overheat when worked too much as in big hills or towing unless there is a way to dissapate the heat. Running it through the rad where temps are around 190-200 or so is OK since the tranny will be just fine in temps about 200 to 250. Even running through a 200 degree radiator, it is still cooling even if slightly.
P/S on the other hand runs a lot cooler and is not designed to handle the temps or pressures that an auto trans can. A typical P/S system will not reach 200 degrees unless it is affected by a close proximity to the engine or exhaust. My point is that unless you have a P/S system that runs over 190 degrees or so, running it through the radiator will not cool it, it will only heat it when the demand on the P/S system is light and the engine is at normal operating temp.
Your rig does not sound like it has a "typical" P/S system. However, I would still not recomend running the P/S fluid through the rad. Big tires, low pressures, wheelin.... yeah I would definately recomend a fin style remote tranny cooler for you since it is completely seperate from the cooling system.
The reason these things fail (in general) is because of heat. It breaks down the viscosity of the fluid and you end up with an oil that has the viscosity of water. It will leak through all your seals and at that point, you've lost all the hydraulic principles of the oil which made it work in the first place. I use type 'F' tranny fluid in my P/S system. I believe that it has a higher temp threshold than normal P/S fluid and it carries the same hydraulic principles."
