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Working out with mild cold

Hi all, I have read many times that working out with a cold below the neck is really bad for you. The thing is, I actually don't feel achy or feverish I just have the last bit of a very mild productive cough which I picked up last week (started with a head cold and then got it below the neck after a few days)

Is it really that bad to work out if your feeling up to it? Obviously I'm not looking to do a heavy HIIT and Strength training session as I've had a few days off so wanted to do some low impact and core work today. Is it really a bad idea to do the above? Or what are your experiances?

Many thanks