OK, Lomcevak, perhaps it's because I'm thick, but I don't think you are explaining the pros & cons, I think you're suggesting something that makes no sense.
So there we are on the downwind leg at a medium power setting and our check for carb icing shows nothing significant.We put the carb heat to cold
So why would you put CH to cold? (I presume we're still talking about PA28s & Lycomings)