I asked this question on here not long ago. I'd say try to workout for 15 minutes and see how you feel and if you feel ok keep going. Keep taking short breaks and pay attention to how you're feeling, you know your body best :)
I ended up with a full on cold that turned into sinusitis and triggered my asthma, so I decided to stay away from the gym until I was fully recovered (which took four weeks!)
Personally, I don't stay away if I'm feeling sniffly/slightly run down because after working out I feel revitalised
If its just a common cold working out will help you recover from the cold faster. I've recently red a study about this. It went on to point out that if u have a fever or are nauseous then def pass on the gym. So that's what I go by. I have a cold as I am writing this and you will find me at the gym after work.