House by a river that's cold (4)
I believe the answer is:
hoar
'cold' is the definition.
(similar in meaning)
'house by a river' is the wordplay.
I cannot really see how this works, but
'house' could be 'ho' (abbreviation for house) and 'ho' is found in the answer.
'a' is within the answer.
'river' could be 'r' (abbreviation) and 'r' is found in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
'that's' acts as a link.
(Other definitions for hoar that I've seen before include "Here are ice crystals" , "A kind of white frost" , "Grey with age; frost" , "Type of frost" , "Rime" .)