1
general::
A hard-hearted, unfeeling individual, one who shows no emotion, as in Not even the eulogy moved him; he's a real cold fish. This expression was used by Shakespeare in The Winter's Tale (4:4): "It was thought she was a woman, and was turn'd into a cold fish." However, it came into wider use only in the first half of the 1900s.
American Heritage Idioms
2
general::
Phrase(s): *a cold fish
Fig. a person who is distant and unfeeling. (*Typically: act like ~; be ~.) • Bob is so dull—a real cold fish. • She hardly ever speaks to anyone. She’s a cold fish.
McGrawhill's American Idioms And Phrasal Verbs