Reckon I have to diasgree to an extent. A cold is viral, and whether you take medicines for it, let it run its own course, or indulge in exercise, it still takes on average about 7 days to cure no matter what you do.
Colds often have a viral impact in the chest, so there is some reason to believe that exercise during that period might do more harm than good. I've tried exercising through a cold, and sometimes I've just left it. I think you need to be a bit cautious. I don't think there are too many sports physios who believe you can 'sweat' the cold out.