THis is why I use spray bottles. you mix up the minimum you need, and it can be stored in my house away from the cold. I try to keep my garage at +3C all winter, but stuff near the walls can freeze on really cold days. (-35C days)...
On the staining issue, if you leave the surface wet it will still stain. Even with the non-rusting additives, it still oxydizes the cast iron, in my experience. So I dry off with paper towels ad give a WD40 squirt to help with the staining. So I use Varsol mixed with sulfated oil most of the time. For these annular cutters they need cooling to cut well, so hence the solulable oil...