I try to change the dino oils on all my machines before storage. Dino oils tend to run off the exposed part surfaces in time, and separate from any condensed moisture, so they can actually contribute to internal corrosion during storage. Fresh oil reduces the possibilty of water problems, and the fresh oils have the strongest film strength, clinging longer than broken down oils. In the old days, the combustion by-products were a big worry, and acids would form in used oil, eating into engine parts, especially bronze bushings. Today's brand name oils contain buffers and other additives which make this type of failure pretty much a thing of the past. That's one of the reasons why we can change oil at 3,000-7,500 mile intervals now, instead of 1,000 miles like when I was a pup.
I do not change my synthetic oils for winter storage. Full synthetics do not separate from water the way dino oils do. Synthetics also have tremendous cling strength, with a film remaining on even unused parts for a very, very long time. My experience in maintenance in a wastewater treatment plant taught me loads about the advantages of synthetics under these circumstances. Once we changed to synthetics, oil changes every three months, whether our machines were operated or not, became a thing of the past.
One thing, if you do change your oil for winter storage, do not start the engine during the winter. All your efforts will be lost. If you do have to run your engine during winter storage, get it to full operating temperature, and by riding, not just idling. You need to get enough heat to drive off all condensation, and you need to heat and move the transmission parts, to drive off moisture and thoroughly coat the parts with oil.