Furry animal may be cold in far-eastern country (10)
I believe the answer is:
chinchilla
'furry animal' is the definition.
(I've seen this before)
'cold in far-eastern country' is the wordplay.
'cold' becomes 'chill' (chill can mean cold).
'in' is an insertion indicator.
'far eastern country' becomes 'China' (country in the Far East).
'chill' inserted into 'china' is 'CHINCHILLA'.
'may be' is the link.
(Other definitions for chinchilla that I've seen before include "little furry animal" , "furry creature" , "(Fur of) a small South American rodent" , "Soft grey fur" , "Rabbit" .)