Sailor, half frozen, stumped by subzero conditions (4,5)

I believe the answer is:

jack frost

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'sailor half frozen stumped by subzero conditions' is the definition.
I can't tell whether this defines the answer.

'sailor half frozen stumped by' is the wordplay.
'sailor' becomes 'jack' (jack can informally mean a sailor).
'half' suggests halving the letters.
'stumped' becomes 'st' (cricket abbreviation).
'by' is a charade indicator (letters next to each other).
'frozen' cut in half is 'fro'.
'jack'+'fro'+'st'='JACK FROST'

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(Other definitions for jack frost that I've seen before include "Personification of freezing weather" , "Freezing weather personified" , "Winter personified" , "Cold weather, personified" , "nipper" .)

I've seen this clue in The Times.

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