See how often they participate in the script: HERE.
Character Story: A cat belonging to Jovani. He becomes cursed along with his master when Jovani sells his soul for riches. Link eventually helps break the spell and it is revealed that Gengle is the leader of the gang of cats in Castle Town.
Race Story: Animals appear all throughout Hyrule and are often often helpful in their own ways, either directly or through subtle advice. Link can talk to them when he is in his wolf form.