I decided today that I really want one that is a wool cooler with a waterproof, breathable outer. Not necessarily even waterproof, just slick.
I work horses, put a sheet on them and turn them out....they roll....sheet gets really dirty (especially if it is damp). So if the cooler had an outer layer I wouldn't cringe as I turn them out.
For what it's worth I don't turn them out in wool coolers, I would, however, prefer them for when they are still damp after working.