Horrible cold undies worn by son kept under wraps (11)
I believe the answer is:
undisclosed
'under wraps' is the definition.
(thesaurus)
'horrible cold undies worn by son' is the wordplay.
'horrible' indicates an anagram.
'worn by' indicates putting letters inside (outside letters are worn by those on the inside).
'son' becomes 's' (genealogical abbreviation for son).
'cold'+'undies'='coldundies'
'coldundies' is an anagram of 'undiscloed'.
'undiscloed' enclosing 's' is 'UNDISCLOSED'.
'kept' is the link.
(Other definitions for undisclosed that I've seen before include "not accessible" , "Not made known" , "Not revealed" .)