the problem is two fold: the nose dryness issue as well as the infection that may or may not have caused it. the infection may be either systemic or localized to the nose. it could be that she flipped over a rock or something that had a plant/ fungus that was toxic or to which she was allergic. the dryness and infection problem can be attacked by using polysporin or bactrim or some antibiotic in an emolient cream. Polymicidin, gramicidin and anitfungal products like nystatin can be used. sometimes a little bit of vaseline would work. in either event, put the stuff on while she is going to stay inside as she would otherwise just get her nose covered again with goop. some people have put the products on the inside of their pet's nose. a little bit goes a long way. Knowing dogs, she will probably try to lick it off. It sounds as if the problem is localized to her nose as you have described no other symptoms. A systemic infection would manifest itself in vastly more noticeable symptoms- sluggishness, colorful and/or purulent discharge, ear infection etc...she should be given water more often than she is currently; sometimes dogs dont' drink as much as they should. a trick to get her to drink more water is to put a small amount of 2% evaporated milk in her water. maybe 15 ml or a tbsp would do the trick.
i have seen one dog ( bulldog ) with such a dry nose that it had cracked so much that it looked like a very old straw broom. Rather ghastly looking but the dog didn't seem to mind and his owner didn't seem to notice.
have you noticed any other changes in your dog's coat or nails? any problems on the skin such as small scales or circles? itchiness?