Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry that your girl Sassi develops a rash on her nose when she goes outdoors.
In young cats with raw nose lesions that seem to come and go periodically I would be most suspicious of autoimmune conditions (body attacking itself) such as vasculitis or pemphigus. These can be triggered by UV exposure. These are diagnosed via biopsy and treated with prescription immunosuppressive drugs. So she would need a veterinary visit to get biopsies or medication.
The most common one we see in cats is Pemphigus Foliaceus. This usually begins with lesions somewhere on the head, especially the nose leather, ear tips, chin and around the eyes. It can also cause lesions on the foot pads. Treatment is steroids, but sometimes we need to add another immunosuppressive drug like Chlorambucil.
Because her lesions are only on her nose we may just be able to use a topical immune suppressive drug like steroid creams or Tacrolimus.
In the meantime I would supplement her diet with omega 3 fatty acids to help heal her skin. Dose her based upon the EPA (eicosapentanoic) portion of the supplement at 20mg per pound of body weight daily. If you do that the rest of the omega 3's in the supplement will be properly balanced. The supplement label should break down how much of each omega 3 it contains per dose, if it doesn't then it likely isn't a quality supplement. For example if she weighs 12 pounds she needs 240mg of EPA per day. If the supplement has 200mg of EPA per dose then she would need roughly 1 & 1/4 doses of that supplement per day (capsule, capful etc).
Another possibility if these lesions are only on the leather part of her nose, since she goes outdoors and she is a light colored cat, is a sensitivity to the UV rays in sunlight, known as solar dermatitis. This can progress to a type of cancer called squamous cell carcinoma so we do want to limit her UV exposure (try to keep her in between 10 am & 4 pm) and apply sunscreen safe for babies if she does go outside in the daylight hours. To ease the discomfort of already present lesions puncture a vitamin E capsule and dribble the contents on her nose sores. Solar dermatitis can be diagnosed definitively via a biopsy.
If this has progressed to squamous cell carcinoma then ideally surgical removal of the affected tissue is recommended. In some cats that isn't possible because of the extent of the lesion. In those cases we use moisturizers to keep the nose soft and more comfortable, supplement omega 3 fatty acids (dosed the same as recommended above), and use pain medication as needed.There is a new therapy that is experimental called Photo Dynamic Therapy. It uses a laser to selectively destroy cancer cells after the cat has given been a chemical to identify the cells. There is an animal hospital in Santa Barbara, California that offers this therapy. Here is a link to their website and an article about squamous cell carcinoma as well as a blurb about Photo Dynamic therapy at the end. http://www.lbah.com/word/squamous-cell-carcinoma-scc/
I'm not sure where you are but you may find a veterinary oncologist or dermatologist that offers this therapy in your area if her lesions ever progress that far.
Other possibilities are a deep fungal or bacterial infection. That wouldn't make sense with her if the lesions seem to come and go on their own but I mention them to be complete. If we are concerned about infections ideally she would have cultures with sensitivities taken of the area to diagnose the root infection and make sure we are using appropriate therapy.
Finally recurrent Herpes virus flares can cause crusts and sores on the nose, especially on the furred bridge of the nose. This seems less likely with her as it sounds like her lesions are more on the leather part of her nose.
In short it sounds like your girl needs to see her veterinarian for a definitive diagnosis because her lesions are recurrent.
In the meantime keep her out of the sunlight during the day and give her an omega 3 fatty acid supplement.
Best of luck with your girl, please let me know if you have any further questions.