Ghengis is very right. "Even" a cold will really degrade your flying ability. I've spent twenty odd years telling anyone who will listen that they should not fly with a cold.
But then your company "suggests" that for your future employment prospects you go flying and you do, and you perform way below your ability and you go home feeling worse. Or at the private flying level on a perfect evening you take the machine out of the hangar for a sunset flight, and you screw up. There is always a reason.
Hopefully this is a good lesson for you as a future instructor (We read your mails, we know you'll get there...) that if you have a trainee with a cold, send them home. At best it will be a poor lesson and you'll catch the cold- at worst they'll do something out of character and catch you out.
My 2c's