From TM-9-2320-212-10 Operator's Manual page 1-5
or the older TM 9-8030 Operation and Organizational Maintenance page 19:
The truck has a "recommended towed load (max)" of 6000# in highway or 4000# off road. Since the only hitch on the truck is the pintle hitch it stands to reason that it is rated for those weights. I've heard reports that back in the days when these trucks were in active duty people regularly towed more than that. I would not hesitate to tow the rated load if the pintle and rear cross member were in good shape.
One advantage of the pintle hitch is that there is no "drop" as you sometimes have with a receiver hitch when using a dropped insert. So the pull is always very close to a horizontal pull. There is little or no twisting force on the rear cross member as there would be if using a receiver hitch mounted to the cross member with a large drop.
One important consideration: it's not just about what you can tow, it's about what you can stop. Your brakes need to be in good condition and properly adjusted. I had concerns about the drum brakes on some of our long down-grades here, so had a disk brake conversion done on my front brakes and a vacuum power boost system added for better braking. I also added a brake controller, and my heavier log trailer has electric brakes. It's been a great combination. (I'd like to add electric brakes to my little dump trailer, but haven't looked in to it yet.)
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A little topic drift from your question on the pintle hitch:
I don't own a trailer that uses the pintle hitch. I saw where some places sell a receiver that bolts on in place of the pintle hitch and another that has a piece sandwiched between the pintle and the rear cross member that drops down and puts a receiver tube below the pintle. I was VERY leery of using something like this with a heavy trailer, since the pull is no longer horizontal back from the rear cross member. It puts a twisting moment on the the rear cross member, and that force gets even worse if you use a dropped insert in the receiver to get the ball at a "normal" hieght above the ground (even more so on my truck, since a large drop is required due to the 11.00x16 tires.) That sort of torque on the rear cross member is not something I would want to risk.
Since I did not want to risk twisting the rear cross member, I installed a modern, frame-mounted receiver hitch (modified to not lose so much ground clearance that most modern receiver hitch set-ups have if just bolted on to the M37 frame as-is). This puts no strain on the rear cross member, despite the 7" drop used on the receiver insert.
I have regularly towed 4000 # loads (3000# of stone in a 1000# trailer) both on the road and in the woods. Usually only a +/-10 mile trip.
I have occasionally towed +/-6000# pounds in my log forwarding trailer. This trailer is equipped with electric trailer brakes, and a brake controller is installed in the truck. I've had no difficulties (though the person stuck behind me when I'm going up a hill might have a different opinion on that).