Cut No Ice Meaning

(idiomatic, usually with "with") To have no influence (on).

Example: 1917, Arthur Conan Doyle, “His Last Bow”, in His Last Bow:
  It cuts no ice with a British copper to tell him you're an American citizen. 'It's British law and order over here,' says he.
1920, Virginia Woolf; Anne Olivier Bell (editor), The Diary of Virginia Woolf, published 1984, page 72:
  It's a feeling of impotence: of cutting no ice. Here I sit at Richmond, & like a lantern stood in the middle of a field my light goes up in darkness.