3340 with oil in Hydraulics

I have a 3340 that gets oil in the hydraulic system. Radiator is never low so I ion't know where it comes from. Water will not let hydraulics move in the winter unless the tractor runs for hours to warm up. I've changed all the oil last year and it looks just as milky this year. Not looking forward to cold weather when things won't work. Please help!!
Is there an oil cooler built into the bottom of the radiator on a 3340? Could water be coming from there? Radiator never seems low.

No, but how many implements have you contaminated with milky oil before changeing it ??

I would tap it off and leave the water to evaporate in an open bucket, in this time of the year, in front of a stove is best i suppose.