Lets hear your suggestions for a winch for a car trailer.

In my experience the cover just makes the corrosion worse by trapping moisture. That said I'm admittedly reactionary when it comes to winch preventative maintenance.
I tend to forget about the winch on my truck until it is required to proceed. Bad habit!
I have never had any issues with corrosion by covering them, any moisture trapped will be dried out by going down the road.