Material left in bed covering horse's head (5)
I believe the answer is:
cloth
'head' is the definition.
(thesaurus)
'material left in bed covering horse's' is the wordplay.
'material left' becomes 'l' (common abbreviation. I am not sure about the 'material' bit.**).
'in' indicates putting letters inside.
'bed' becomes 'cot' (cot is a kind of bed).
'covering' is a charade indicator (letters next to each other) (on top of in down clue).
'horse' becomes 'h' ('H' can be a synonym of 'horse').
'l' going into 'cot' is 'clot'.
'clot'+'h'='CLOTH'
(Other definitions for cloth that I've seen before include "Sails" , "Gingham, say" , "The clergy" , "rag" , "ministers" .)