Shelter in filthy area with freezing water (6)

I believe the answer is:

sleety

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'freezing water' is the definition.
'sleety' can be an answer for 'freezing' (thesaurus). I'm unsure of the 'water' bit.

'shelter in filthy area' is the wordplay.
'shelter' becomes 'lee' (as in lee side, the side sheltered from wind).
'in' indicates putting letters inside.
'filthy area' becomes 'sty' (I can't explain this - if you can you should believe this answer much more).
'lee' going within 'sty' is 'SLEETY'.

'with' acts as a link.

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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