ALWAYS use grease on an anchor winch.
Yes grease can harden on the surface, but apply pressure to it and you will find it slides. Try it. This is the main function of grease - Greases are a type of shear-thinning fluid, the viscosity of the fluid is reduced under shear. When pressure is applied, the viscosity drops to that of the lubricant in the grease, the mineral oil. Grease is basically emulsified oil that stays in one place and lubricates when needed. Oil does not stay.
As for dust and grit, oil will attract this as well. The difference is, oil will transfer it into the bearing whereas with grease it will mostly stick to the outside.
Oil will also leave the bearing (both slowly and rapidly) and put itself on your deck, with predictable results. Again the function of grease is to stay in the place it is applied.
Grease is specifically designed for this type of use - open air simple bearings. It is of course even used in sealed bearings. Oil is used where it can be automatically replenished and re-circulated.
So I can't understand why anyone would use oil instead of grease. If you do that you would surely never use grease anywhere.
Ironically the solution in [i]very[/i] dusty or gritty environments is to use [i]thicker[/i] grease. Never oil.
David