Interesting
article in the Times. The answer seems to be: a head cold does not affect your lung functions or your exercise capacity (even though you feel fatigued). If you have a feer, muscle aches, or chest congestion, OTOH, exercise is probably a bad idea, and pushing yourself is definitely a bad idea.
If you do have just a head cold (sneezing and runny nose), exercise will probably make you feel better, but it won't actually make you better faster.