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Cold and wet, shelter found in home on farm (6)

Ross

I believe the answer is:

sleety

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'cold and wet' is the definition.
(I've seen this before)

'shelter found in home on farm' is the wordplay.
'shelter' becomes 'lee' (as in lee side, the side sheltered from wind).
'found in' is an insertion indicator.
'home on farm' becomes 'sty' (I am not sure about this - if you are sure you should believe this answer much more).
'lee' inserted within 'sty' is 'SLEETY'.

Can you help me to learn more?

(Other definitions for sleety that I've seen before include "Cold and wet" , "Such wintry weather" .)

I've seen this clue in The Times.
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