I have a friend who was on prednisone off and on for years, because of autoimmune hepatitis. She was on such a high dose that AFTER she had a liver transplant, the level of immunosuppressants she takes is actually less than what she was on before.
From her experience...
She would rarely get just a cold. Her immune system was pushed down so it wouldn't respond. "Being sick" is the symptoms of the immune system fighting things off...blowing the nose, coughing stuff up, because the body is battling it and is creating waste products...those are positive signs. She didn't do those things when her body encountered a normal germ.
I should mention that b/c she didn't react...she was a serious "Typhoid Mary". She would spread stuff from work to friends and back again. When she was on the strongest doses, I was getting sick all the time, because the stuff from her work would jump to me when she would visit. Awful awful.
When she DID react, it was bad. If a germ was strong enough to cause an immune reaction in her, it was nearly the plague.
Before her transplant, during the few years she spent on, off, and on the list (she got better for a few years after her divorce), she had to follow their guidelines, which meant near constant vaccines. They'd jab her, test for immunity. Would find none. Jab her again. etc etc. I kept wanting to go with her to appointments to ask them why on EARTH they were expecting an immune response when they had her on so many immune suppressing drugs. OF COURSE she wasn't responding. (so she, with a LIVER problem, got alllll of the extra gunk in the vaccines, all the preservatives and metals and all of that, with NONE of the supposed benefits...makes no sense!) She never let me go, because she had to toe the line with the program. But I felt bad for her!
Now she has a new liver and more of an immune system, since the steroids are lower than they were before (which is just so disturbing, but she was really really sick in that last year or two). She'll catch some normal colds. Her body has changed, too...all very in line with the more interesting aspects of organ transplant (different food likes and dislikes, etc), and some just a sign of a functioning body (she sweats now...never had before). And catching the occasional cold is one of them.