It doesn't take a lot of water to turn the oil grey.
Condensation usually doesn't produce enough water to make the oil grey............I would suggest changing the oil and running it hard enough to get the engine to operating temp, then run it for a couple of hours at operating temp to boil out any residual.
If it stays grey or becomes grey again, I would say it's leaking in ( from someplace) If the boat stays outside, look for a path for rainwater into the engine compartment....It DOES rain here once in a while in the Great Upper Left Coast!
Put a pressure gage on the cooling system and see if it's maintaining pressure after a shutdown.. (7, 10, 13 psi etc) If the pressure drops it's leaking someplace.
It's also unlikely you would get any water in the oil through a leaking oil cooler. The oil pressure is MUCH higher than any water pressure that might be on the cooler. You would just lose oil overboard through it if it was leaking.
You could also have leaking riser gaskets, risers and/or exhaust manifolds but the amount of water is usually limited to what is in the manifolds/risers immediately after shut-down. I had that problem with my previously installed OMG 460. If I tried to start it within 20 min or so of shutdown, it would briefly hydrolock then start after a couple of tries.
The amount of water wasn't all that much and never turned the oil grey and since I was usually driving the boat after shutdown, that little bit of water in the oil (that got past the rings) evaporated out in short order. If I waited over night (or longer than about 30-45min) the engine started normally indicating that the oil leaked past the rings in that amount of time.
