Cat sheltering in cold bar, one in Ohio city (10)
I believe the answer is:
cincinnati
'ohio city' is the definition.
(I've seen this in another clue)
'cat sheltering in cold bar one' is the wordplay.
'sheltering' is an insertion indicator.
'cold' becomes 'C' (eg on taps).
'bar' becomes 'inn' (both can mean a drinking establishment).
'one' becomes 'i' (Roman numeral).
'in'+'c'+'inn'='incinn'
'cat' enclosing 'incinn' is 'cincinnat'.
'cincinnat'+'i'='CINCINNATI'
'in' acts as a link.
(Other definitions for cincinnati that I've seen before include "US city" , "American city" , "home for some Ohioans?" , "US location" , "Industrial city on the Ohio river" .)