Working out and the Common Cold

When suffering with what might be considered a common cold, does working out help, hurt or is it of no consequence?

Mild head cold, yes. A very mild workout.
A chest cold, no. Rest.

The rule I always heard was - sick from the neck up? Go ahead (it actually helps with congestion), neck down? STOP!

Also, if you have a fever, your body is fighting something, let it work on that.