Bed cold: that's painful (5)
I believe the answer is:
couch
'bed' is the definition.
(I know that couch is a type of bed)
'cold that's painful' is the wordplay.
'cold' becomes 'c' (abbreviation, eg on taps).
'that's painful' becomes 'ouch' (I've seen this before).
'c'+'ouch'='COUCH'
(Other definitions for couch that I've seen before include "Long seat; grass" , "Upholstered seat for more than one" , "something comfortable to sit on" , "Grass; reclining seat" , "express" .)