It sounds like you have the infamous battery acid corroding the oil cooler problem. I had that happen on my 4200 shortly after I bought it, and fortunately it was corrected under warranty.
Carefully check for the leak using cardboard, I use drywall shims for that purpose if it's not blatantly obvious as to where the leak is coming from. If you have the old fashioned battery with caps for adding water, then get a new sealed maintenance free battery. You're still stuck going to Deere for a battery as they used an odd size that isn't readily available in the 4200 - 4400 series, or fabricate new battery mounts for a more common battery group size.
Check for acid corrosion on the cables and elsewhere if that is the cause of the leak.