rhinophyma

Hypertrophy of the nose with follicular dilation resulting from hyperplasia of sebaceous glands accompanied by fibrosis and increased vascularity.

The noun has one meaning:

Meaning #1: enlargement of the nose with dilation of follicles and redness and prominent vascularity of the skin; often associated with excessive consumption of alcohol
  Synonyms: hypertrophic rosacea, toper's nose, brandy nose, rum nose, rum-blossom, potato nose, hammer nose, copper nose