I hate to disagree with the advice given above, but I have read (somewhere) that oil is not useful in servicing winches, as it is likely to migrate out of the place where you want it, and into places where you don't (specifically the bearings).
The recommendation is to use a light coating of grease, and no oil.
CAVEAT: this may only be true for Andersen Winches (with which I am most familiar), but it makes sense to me.
You are correct. IMO the majority of info out there on winch lubing is "Conventional Wisdom" and/or out of date. I attach a post I did a while back on the subject.
As far as winch lubrication goes, I'd like to add a bit of "against the grain" info here. I now exclusively use white lithium grease on my winches. I have tried everything over the years - water pump grease, insanely overpriced "winch" grease from the manufacturer, PTFE grease etc. etc.
The white lithium is actually a cream colour and has a consistency about like stiff yogurt. I currently have a cup of Gunk brand and it is specifically recommended for boat winches. You have to be sure to get some with this colour and texture. I have also seen "white lithium grease" that was much more like the usual grease you see - more of a dark amber colour and very stiff, like wheel bearing grease - DON'T use this stuff.
It goes on cleanly and stays clean - doesn't trap dirt like the other stickier greases. It also leaves everything freer - the winches turn noticeably more easily. Its lower viscosity than the other commonly used winch greases gives it these attributes. I've been using it for at least 20 years now and have NEVER had a spring or pawl or any other failure on a winch greased with it.
Here's the sacrilege - you can GREASE your pawls & springs with it. A light coating clings better than oil but doesn't cause the stiction that heavier greases would (and which is the reason for the conventional wisdom of oil only on them). This has the added benefit of quieting the winches - the pawls go tic tic tic instead of clink, clink, clink.
I grease everything quite heavily, reassemble the winches and rotate them several times, pop the drums off again and wipe off all the "squeeze out", then reassemble. That gives the exact right amount everywhere internally.
It has the added benefit of cleaning up easily when you strip the winches next time - no wire brushes needed to get the dried crust off things - everything rinses clean in solvent or diesel.
Only one lubricant needed for everything, including your throttle cables, shift mechanisms, steering cables etc. as well. A cup of it costs about $5 and lasts for about a decade - try it, you'll like it a lot.
As for PTFE greases (Teflon), a friend who was in the bearing business for decades said it should NOT be used on caged roller bearings. It is so slippery that the rollers tend to skid instead of rolling.