I had an initially mild cold and basically trained through it for a few days, feeling a little worse after about five days but good enough to keep on my schedule. Of course like an idiot I worried more about missing a workout than anything else.
Long story short I woke up one morning with a 101.5 degree fever and a sinus infection. Looking back I wish I had taken a day or two completely off and just rested. My unimpeded training simply weakened my immune system to the point the cold kicked into high gear.
Anyway, be careful with that old rule of thumb about training through a cold if it's above the neck and you have no fever. Didn't work well in my case.