One doesn't believe it's cold through the month, almost freezing! (7)
I believe the answer is:
sceptic
'one doesn't believe' is the definition.
(I've seen this before)
'cold through the month almost freezing' is the wordplay.
'cold' becomes 'C' (eg on taps).
'through' means one lot of letters goes inside another (inserted letters go through the word).
'the month' becomes 'sept' (Sept is an example).
'almost' means to remove the last letter (almost the whole word is kept).
'freezing' becomes 'icy' (synonyms).
'c' going into 'sept' is 'scept'.
'icy' with its final letter taken off is 'ic'.
'scept'+'ic'='SCEPTIC'
'it's' is the link.
(Other definitions for sceptic that I've seen before include "Greek philosopher" , "One doesn't believe" , "Someone inclined to disbelieve" , "One might doubt it" , "Thomas for one" .)