How do you store your winches?

I made a compact cover out of sheet aluminum just to keep the sun off my synthetic line. Won't trap moisture either.
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In the photo above I have the hook attached to the bar on the winch plate. I didn't like the thimble up against the fairlead like that, so I made a polyurethane stopper out of a caster wheel - the cheap guy's safety thimble.
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The cover for the rope is nice. If I had a cover on mine, that would be it.

And the caster wheel/stopper is very smart. Without it, the type of thimble your rope has can gouge the hawse, especially if it is aluminum. These gouges can snag the synthetic rope and cause it to snap. That is one of the hidden design features of the Safety Thimble.
 
We have winches on all of our heavy rescue rigs and having spent the better part of 25 years riding them I have learned (through experience and talking with Warn) on how to store the cable/rope. First is, winches are aluminum (except for the drum and the gears inside and the motor housing), getting wet is not a big deal, in fact they have "grooves" machined into them to allow water to drain out should they become submerged. Covering the winch is a personal choice, by no means necessary, just whatever you want to do. Personally I do not cover it, all off the covers I have seen are either neoprene or vinyl and do not allow moisture to evaporate (more worried about the solenoids and the wiring connections than anything else). One thing to consider is that Warn recommends not keeping tension on the rope/cable when being stored. Apparently there is no need to have that "strain" on the components for long periods of time....? I keep my stock thimble looped over a tow hook with the slack spooled in enough that it can be un-hooked but is not so taught that there is strain on the rope..... just my 2 cents.....