I think this is a judgement call. I've heard lots of recommendations - exercise if you don't have a fever, don't exercise if the cold involves chest congestion, but working with head congestion is OK, all kinds of things. I don't know if any of them are true.
If you have to go to a public place to work out (like a gym), DON'T. Please don't! Nobody else wants your germs. You might think you will be as careful as can be, but there is really no preventing cold germs from spreading in a public place like a gym.
If you can work out at home, and you really think a workout will make you feel better, I'd say go for it, though. Maybe go at a lower intensity than normal if you feel yourself getting overly fatigued.
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