Dictator's healthy cold shower (4)
I believe the answer is:
hail
'cold shower' is the definition.
(hail is frozen rain)
'dictator's healthy' is the wordplay.
'dictator's' shows a homophone (sound like) (as somebody dictating would pronounce the word).
'healthy' becomes 'hale' (hale can mean fit and healthy).
'hale' sounds like 'HAIL'.
(Other definitions for hail that I've seen before include "Hard Rain?" , "wintry weather" , "Say hello to the ice pellets" , "weather forecast?" , "Welcome (icily?)" .)