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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' indicates putting letters inside.
'home on farm' becomes 'sty' (I can't explain this - if you can you should give a lot more credence to this answer).
'lee' placed into '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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