So the local (Abernathy) JD mechanic said there were four possibilities:
1) Contamination. Someone put water in the tractor with a contaminated bucket. Unlikely, but he recommended that we siphon the oil out, then run it to see if oil reappears.
2) Water pump. Unlikely,while pump is geared to engine, and thus has a possibility of contamination, any leak will likely come out the weep hole. Will check hole for leaks, and make sure it is clear.
3) Oil cooler. Unlikely, as he says he's only seen that once. However, from looking at the parts catalog, it looks pretty easy to remove. Eight bolts, four o-rings, and three gaskets. It might be worth checking before calling for the $100 truck ride to the dealer.

4) Head gasket. Sadly, this is apparently the most common failure. Near the rear of the head, there is an oil passage going up to the valve train. No way to check this without eliminating the other three, then pulling the head.
I can't check on the tractor until at least late next week, so I'll have to keep you guys in suspense as to the final diagnosis.