Thanks for trusting JustAnswer.com with your concern about your Corgi. Of course, I can not see your dog and no one, not even a canine vet be sure of a diagnosis when not seeing the dog in a face-to-face examination. But I can give you the most likely causes and a course of action to follow to help your friend the best way possible.
Dry and cracked skin on the nose can be the result of cold winter weather or even low humidity indoors. This is often called "snow nose" or "winter nose" because it frequently happens in winter time when the air is less humid, the wind is cold, and it is easy for our dogs to poke their noses into snow or grass with frost on it, beginning the process of dry, flaking nose skin. After all, dogs poke that nose into everything!
Winter nose can result in the top layer of skin peeling and showing new, pink skin beneath. If this is the cause, you must be cautious about having her out in bright sunlight for very long since she could quickly burn her pink nose.
You can apply a thin coat of petroeum jelly (vaseline) several times per day and keep her out of the sun except long enough to do her business by taking her to spots in the shade to walk and exercise for a short period of time until her nose heals and turns black again. If she needs to be outdoors in the sun for longer, you will need to add sunscreen that is non-toxic. Also, beware of cloudy days because the UV rays of the sun come right thought clouds and even though you do not feel the direct sunlight rays, they can still burn her (or you) quickly if not protected.
The chap stick you are using is really not a bad idea at all and very logical, especially if you used chap stick which contains sunscreen. If she licks the petroleum jelly away, you could go back to the chap stick or use a non-toxic moisturizer with sunscreen to protect her nose until it returns to normal. There are lots of choices in non-toxic sunscreens. Just read the label and be sure they say they are non-toxic to children and they will be safe enough for your doggie.
I suggest you try one of these remedies for a few days and if you do not see an improvement, then you need to look further by visiting her vet right away. Even if you see an improvement yet the problem is not resolved within about seven days, then you need to see the vet. Also, if the weather changes and become humid and warmer but the problem returns again for no apparent reason, she must be taken to the vet so other causes can be looked into.
It is even possible that she cracked her nose against something or was somehow traumatized and has peeled as a result. She might have sunburned her nose if outdoors a lot. But it is much more common that the cause is dry skin.
There ARE a few causes which could potentially be quite serious which could cause these symptoms but they are not nearly as common. Abnormal thyroid hormone levels can result in nose color change as well as the dry skin and a vet would have to test her thyroid level using a blood test to determine this and prescribe medication that could help the problem. This is not terribly common, however.
Some immune disorders can cause these symptoms also and that is another area that only a vet in a face-to-face visit can address. Again, this is not the most common cause.
If I can help further, please use "reply" after accepting this answer. I do hope your little lady's nose returns to its normal healthy black, moist condition quickly.