I use the cardboard sleeves on the cold cups for the same reason as the hot cups... it get's too cold to hold. It also keeps the sweat (the moisture that collects around the cup) off my hands.
I printed one out at 100% to see if it will fit the cold cups. Unfortunately, I broke one of the web thingies while trying to free them up. When I reprint it, I'll resize it appropriately, to fit the cold cups, if needed.