Fur spreading over the skin is read as a return to instinct, or a need for warmth and protection. Folk tales of transformation give it a sense of becoming wilder than usual.
When this appeared in your dream, what were you feeling?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.