Coolant in the oil (you said you were losing coolant?) is usually a leaky head gasket. Salt water in the oil would be a heat exchanger, unless you did my mod and cool your oil with coolant, then coolant in the oil could be a cooler.
You can tell for sure by pressurizing the system. I don't know if you can rent one, but a small pump attaches to where the radiator cap goes and you pump it to the appropriate pressure and listen for the leaks.
Will you do the repair yourself? The head will be heavy so you will need some muscle to help you, but I don't think a head gasket is that hard. I've done a few on smaller, gasoline engines.
You will need a head gasket, an exhaust gasket, an intake gasket and maybe a valve cover gasket. Buy them somewhere that you can take em back if you don't use them. You will need a manual for torque settings and valve clearances, get a bag of shop towels, a new oil filter, 5 gallon pail of oil and some new coolant. Scrapers to remove old gaskets, buckets to put bolts in (lest the bilge ferrets get you).
Paint for the block (why not? It will be easy when apart) and any new hose clamps and hoses, belts etc that you will find substandard. Feeler gauges for the valves.
Ever had the injectors serviced? Good time for that. You will need new copper washers for those.
Personally, except for the aggravation and the bad timing (summer) it is an exciting and interesting repair that will let you learn way more about your engine. Shouldn't even cost very much (except for the injector service). Make sure you have good knee pads and a good support system with a good source of coffee (or your favourite beverage).
Not knowing anything about John Deeres, you might have to buy new head bolts if they are "stretch" bolts.
Have fun and don't panic, you caught it before too much damage could occur.