Here is what I do.
Gas or propane generator: change oil and worry about the filter later if it's not causing problems or is relatively new.
Diesel generator change oil and filter, bec. the filter is more a water separator and therefor prone to freezing (can be more complicated but these are the basics).
No matter what type generator you have give it a good workout and drain the oil from the warm engine.
You want to change the oil before winter (or at the end of the season) to flush the acids, water and other contaminants out with the oil to prevent corrosion inside the engine. With the fresh oil in the crankcase let it run for 1/2 to 1 hour, check your oil level and done.
2013 RAM 3500 Dually Longhorn
2014 Trilogy 3650RL, W/D, Onan 5500, 8000# Axles, IS, 960 Watt Solar, 6x6 Volt Battery Bank, Freedom SW 3012 Inv/Charger