As a general rule of thumb If a cat's nose is cold and wet it is healthy, If it's dry and warm, she/he might be ill. Unless it's really hot outside, in which case, the warmer weather is likely to have dried the dampness up so then don't worry about it.
If your cat has a cold of cat influenza however, it could have running eyes and a very wet nose, so it is important to look at your cats behaviour, how is it compared to normal?
There are other signs to suggest that your cat is poorly.
If your cat is in pain, as they cannot communicate this to us or even understand the pain themselves, they are likely to lash out at you by biting or scratching uncharacteristically. So if this happens be on your guard.
Secondly, if your cat keeps going off to dark corners and wants to sleep and be left alone, then it would be best to take it to a vet to get a full diagnosis. This can be difficult if they don't want to be touched and it seems that they are poorly, but you must remember that these are small creatures and cannot go without their food or drink for long at all.
If your cat has stopped eating and drinking, then he could just have toothache, but again it could be more serious, so take him/her off to the vets.
I have known cats to have a perfectly damp nose but still be poorly, so Id concentrate on his or her behaviour, how it's changed,.