I remember our old Woolworth's store serving tea in individual pots with metal cozies but have never seen a sugar bowl with one.......until I googled 'sugar bowl cozy'. it could be that someone decided that's what they'd call it, because it's the only one that turned up. Or it could be that's what it actually was, but few survived.
BTW, my Woolworth's tea pot memories would have been from the late 50's