I used to worry about this a lot (I grew up with cats, but when I started living alone and I was the only one caring for my cat, I started to worry more about every little thing my cat did or didn't do). So, I did some research and talked to my vet.
Since a cat's nose is right there on the outside of their body, its qualities are going to change a lot with the temperature or humidity etc. in its living space. For example, in the winter my cat sleeps near a heater a lot, which leaves his nose drier than when he sleeps other places during the rest of the year. It's like how your own nose can get dry and possibly sore in a dry environment, and change when you are in a warmer or more humid environment.
My vet told me that while it can indicate illness, it is really not the best indicator, as so many other things affect the cat's nose. It is better to look at the rest of the cat, and see if they have other signs of illness, like lethargy or they're not eating or they are indicating they are in pain, and so on. Their noses aren't really a "I am sick" or "I am well" magic button - they are subject to outside environment factors just like human noses.