Nip on part of face by a rodent (10)
I believe the answer is:
chinchilla
'rodent' is the definition.
(chinchilla is a kind of rodent)
'nip on part of face by a' is the wordplay.
'nip' becomes 'chill' (nip can mean a chill in the air).
'on' is a charade indicator (letters next to each other).
'part of face' becomes 'chin' (facial feature).
'by' is a charade indicator (letters next to each other).
'chill' put after 'chin' is 'chinchill'.
'chinchill'+'a'='CHINCHILLA'
(Other definitions for chinchilla that I've seen before include "Soft grey fur" , "Rabbit" , "little furry animal" , "furry creature" , "(Fur of) a small South American rodent" .)