Get rid of much of cold that’s upset friend (8)
I believe the answer is:
decimate
'get rid of much of' is the definition.
'cold that's upset friend' is the wordplay.
'cold' becomes 'iced' (I've seen this before).
'that's upset' is a reversal indicator.
'friend' becomes 'mate' (mate is a kind of friend**).
'iced' backwards is 'deci'.
'deci'+'mate'='DECIMATE'
(Other definitions for decimate that I've seen before include "Reduce greatly (by 10%?) in number" , "severely cut" , "Medicate (anag.)" , "Kill one in ten (as Romans did as punishment for mutiny)" , "Aimed etc in order to destroy a large proportion of" .)