It is for sure getting coolant in the oil, so before taking anything apart, drop the oil pan, fill the radiator and watch where it comes down.
Could be the head gasket, could be orings at the bottom of the cylinder liners, could be the block cracked. Need to find out before taking the head off.
If the block and orings look good, it's probably the head gasket.
Once the head is off, if you're not replacing the orings, be sure to bolt the liners down with a couple bolts and washers. The liners just sit in the block, and if one rides up even slightly, it will break the oring seal and they will have to come out and be resealed, quite a job!
I'm sure as bad as the engine is running it's hard to tell much about it, but take a good look before disassembling it. How is the warm oil pressure? Any knocks, blow-by? How is the rest of the tractor? Clutch, transmission, brakes, tires, front end? Try to get an overall picture. If there are other problems, best to find them now, get an idea of the cost. Nothing worse than getting the engine back together only to find another major problem and have to go back in.
As for the transmission/differential oil, the proper level is to the bottom of the round inspection covers below the seat. One should have a dip stick. Chances are there is water in the cases if it's been outside. It gets in around a bad shifter boot. There are 2 drain plugs. You don't want to overfill it, it will get on the clutch and brake shoes. The original oil was 90w mineral oil. The popular replacement is 15w40 diesel engine oil. That is a common gear case, all fill through the plug on top, by the shifter. The big square cover on bottom, that is not a cover, it's the bottom of the hydraulic pump. Don't take the bolts out unless you're taking the pump out. There is more to it than just removing the bolts.
A shop manual will be a valuable investment.
Let us know how it goes!