It depends on how far along you feel the cold.
If I feel like I might be getting a cold, I always up my Vitamin C and Zinc (plus, I always take two multi-vitamins on training days...regardless). I started doing the extra zinc and vitamin C thing for colds a couple years ago and it's worked well. If I do get a cold it doesn't last as long, sometimes I don't get one at all when I think I will...placebo effect, whatever...the increase in dosage works. Take extra of both if you feel one coming on.
I wouldn't go balls-to-the-wall with my workout that day either but I would definintely hit the weight room. It always makes me feel better to get a pump on and get the blood flowing.
Now, if you are for sure sick or you know for sure you are GOING TO get sick, I would take the day(s) off. You body needs rest, fluids, vitamins, minerals, glutamine, etc and the aforementioned are depleted through exercise and weight training.
Just be smart and listen to your body.
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Backstage, '75 Olympia:
Serge Nubret, "I look like I can take you."
Arnold, "Keep looking."