Rule 1: If you have a fever, stay home.
Rule 2: if you are hacking things out of your lungs, FIND A DOCTOR, not a bike.
If you just have a stuffy nose/head cold AND you are the fortunate type that has exercise induced sinus clearing, GO FOR IT. Clear out the sinuses and should clear your head, always does for me. Definitely take it easy though and eat well of course, but I know I ALWAYS feel better after.
If you are the type where exercise makes your nose worse, don't go. You will probably end up with sinusitis or something bad.
Scot