Hi there and thanks for your question.
Every dog is different and this may or may not be something to worry about. Some dogs will have a mild condition called hyperkeratosis which causes rough skin over the end of the nose. It is often helped by applying either vitamin E cream or opening up a vitamin E capsule and applying the oil.
If there are ulcerations on the nose it could be a condition called discoid lupus or pemphigus...you can read more about this here:
Some Golden Retrievers can have rough skin along with a low thyroid level, so you may want to ask your vet about checking her thyroid level.
I hope this information helps! If you have more concerns, just hit reply. Or, if my answer is sufficient, then please hit accept. Thanks!
It certainly could be that it is rough because of the elements. I don't think it would be frostbite though...that usually effects ear tips and feet and tails.
The vitamin E is very very safe, so feel free to try it. If there is no improvement in a week or so it is probably a good idea to have a vet take a look
Hope that helps!Dr. Marie.
You're very welcome! Have a great day!