Cold sore with lip man treated (10)
I believe the answer is:
impersonal
'cold' is the definition.
('impersonal' can be similar in meaning to 'cold')
'sore with lip man treated' is the wordplay.
'with' means one lot of letters go next to another.
'treated' is an anagram indicator.
'lip'+'man'='lipman'
'sore' put after 'lipman' is 'lipmansore'.
'lipmansore' anagrammed gives 'IMPERSONAL'.
(Other definitions for impersonal that I've seen before include "Cold" , "Aloof" , "Cool" , "Objective; disinterested" , "Ignoring one's own feelings" .)