Garret? Starting at the top, it's cold (5)
I believe the answer is:
attic
'garret?' is the definition.
('attic' can be a synonym of 'garret')
'starting at the top it's cold' is the wordplay.
'starting' indicates taking the first letters.
The initial letters of 'at the top its cold' is 'ATTIC'.
(Other definitions for attic that I've seen before include "Classical" , "Top apartment" , "Upstairs room" , "from Greece" , "Classically elegant" .)