Bitter and cold -- dry outside (5)
I believe the answer is:
acrid
'bitter' is the definition.
(thesaurus)
'cold dry outside' is the wordplay.
'cold' becomes 'c' (eg on taps).
'dry' becomes 'arid' ('arid' can be similar in meaning to 'dry'**).
'outside' means one lot of letters goes inside another.
'c' put into 'arid' is 'ACRID'.
'and' is the link.
(Other definitions for acrid that I've seen before include "Nastily pungent" , "Strong and sharp" , "Greek goddess" , "irritating" , "Direly pungent" .)