Snow from burnt coal (4)

I believe the answer is:

coke

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'coal' is the definition.
(thesaurus)

'snow from burnt' is the wordplay.
'snow' becomes 'C' (synonyms).
'from' is a charade indicator (letters next to each other).
'burnt' becomes 'oke' (I am not sure about this - if you are sure you should believe this answer much more).
'c'+'oke'='COKE'

Can you help me to learn more?

(Other definitions for coke that I've seen before include "Drink - drug - solid-fuel product" , "something for heating" , "Carbonised fuel residue" , "Fuel derived from coal" , "Residue from coal used as fuel" .)

I've seen this clue in the Sydney Morning Herald.

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