Cortisone is a bit more complicated than that - it mimics cortisol, the stress hormone. The effects of cortisol are varied and complex - it changes the expression levels (amount of protein made) of over 10% of the genes in your body. Among other things, it suppresses your immune system (which is why corticoids are used for organ transplants, asthma, allergies, inflammation, etc), increases your blood sugar, boosts your metabolism, and diverts resources from muscle/bone growth.
One important thing to understand is that corticoids are administered in many different ways depending on what they're treating. For example, I have asthma, and I take a low dose corticoid inhaler twice a day to basically stop the immune system in my lungs from freaking out over nothing all the time and causing breathing difficulties. Applying the dose where it's needed keeps the dose down and prevents side effects in the rest of the body. Similarly, corticoid creams are available to treat beestings, eczema, etc.
Cyclists however, have been known to get a TUE for the topical cream but then take the much more powerful oral or injected versions, for the aforementioned benefits to blood sugar, metabolism, inflammation, etc.
The most notorious case is probably Armstrong's backdated TUE in the 1999 TdF, allegedly for a saddle sore.
TUEs are also granted for oral corticoids, for example Chris Froome in the Tour de Romandie this year. They're a standard treatment for acute asthma aggravated by colds, flu, chest infections etc. I have some sympathy for Froome in this case - I've been given the same treatment (prednisolone) a bunch of times for chest infections when I was in pretty bad shape, and calling it 'horse steroids' like some Clinic members do is a cheap shot - aspirin is used to treat horses but you wouldn't call aspirin 'horse painkillers'. It worked very well and possibly saved my life on a couple of occasions, but any time I needed prednisolone, I could barely climb the stairs, nevermind a Cat 1 mountain.
As cortisol is a 'fight or flight' hormone released in short bursts when the body needs energy, you can probably guess that long term use of corticoids is bad for the body. It can cause wasting of bone and muscle,
thinning of skin and also joint damage, especially if used to 'play through pain' (look at all the 80's cyclists with bad knees, as well as half the Europcar team, ahem). What's outwardly visible, however, is increased water retention, leading to the classic
'moon face', easily noticeable in a skinny pro cyclist...