I personally change oil in spring when I start to use my cars for the season as I never start my cars during the storage period, why should I do that?
Boats are normally serviced when they are stored for the winter, I’ve never heard about boat engines are started now and the during winter storage.
I don’t know what’s best but spring oil change works fine for me.
Where I lived in the USA, there was a huge difference between "laying up a boat" for winter storage, and an old collectible car. Of course it's different in different climates.
The boat has all the cylinders fogged with a special fogging oil. As boat engines don't generally have a closed loop cooling system, you need to add some antifreeze into the system to get into the "nooks and crannies" to prevent freeze damage. Many also fill the tanks, adding a special additive such as Sta-Bil or Sea-Foam. Bilges are purged dry, pumps are dried, etc. Doing this doesn't lend itself to a quick run around the lake on a nice day in January (even if the lake isn't frozen) since you'd have to repeat all these steps once again.
I suppose some may fog their Pagoda engines prior to winter storage, etc. but mainly you change the oil and fill the tank if that's your chosen protocol. Stabilize the fuel if you choose. If you have a nice dry day, no harm in warming it alll up and taking for a good "Italian tune up". I did not always get a chance to do this...