If it does, it means that water is contaminating the oil, and you probably have a problem with the seals. In this case, take the engine to a dealer. In fact, take the motor to a dealer with any indication of water or metal filings contaminating the lower unit gear oil. Silvera says to extend the steering cable fully, which means turning the steering wheel hard to the right. He recommends wiping WD-40 or on the exposed part of the cable and adding grease to all the grease fittings in the steering assembly.
Water can freeze there and crack the lower unit.
Store the trailer for adequate drainage so that the bow is slightly higher than the stern. The correct inflation pressure is molded into the sidewall. Now is a good time to rotate the trailer tires. This is also the time to add grease to the bearing protectors, or pull the wheels and repack the bearings. Your dealer can advise you whether repacking or replacement is appropriate.