Riding sick not safe or fun!
If you are not feeling well you shouldn't ride unless you have too.
When you feel sick you are not at the top of your game and you will not be as alert as you should be. You tend to more focused on how bad you feel. Your reflexes will be slower and your judgement may not be the clearest. You will be uncomfortable and really would be better off not trying to ride. If you are sick it can be like you are drunk and that is not a good way to ride. Also many over the counter cold medicines contain alcohol in them and most make you sleepy
Plus for those that wear a full face helmet, coughing or sneezing in a helmet is not any fun, and can be messy.