Hood for cold bird (4)
I believe the answer is:
cowl
'hood' is the definition.
(I know that cowl is a type of hood)
'cold bird' is the wordplay.
'cold' becomes 'C' (eg on taps).
'bird' becomes 'owl' (owl is a kind of bird).
'c'+'owl'='COWL'
'for' acts as a link.
(Other definitions for cowl that I've seen before include "Cover for monk or chimney" , "Monk's hood - chimney cover" , "Monk's hood or chimney covering" , "Hood for monk or chimney" , "form of protection?" .)