Can raynaud's affect your nose (as well as the fingers and toes) and if so how do you treat it?

Yes. Raynaud's phenomenon usually affects the fingers and toes, but has been known to affect also the nose, ears, nipples, and lips. The treatment should be the same, identifying the triggers and avoiding the triggers. Auto-immune disorders, drug side effects, occupational situations, and other causes can be treated if they are causing raynaud's phenomenon.
extremity disease. Raynaud's disease is due to spasm of the blood vessel muscular layer due to temperature extremes. It most commonly affects the feet and hands. I am not aware of any effect on the nose. The sensitivity of our faces (and our nose) to temperature extremes may mimic some of the symptoms however.