Green’s Dictionary of Slang

1. (orig. US) to impress, to influence, to make a difference; usu. in negative phr. cut no ice (with), to make no impression, to leave unmoved.

c.1892		S. Crane ‘The Landlady’s Daughter’ in Stallman (1966) 9: ‘Say, Thorpe, Trixell seems to be making the pace for all of us [...]’ Thorpe smiled. ‘Well, he certainly does seem to be cutting some ice.’.
1896		Ade Artie (1963) 56: That cuts no ice in our set.
1899		Ade Fables in Sl. (1902) 21: Moral: A New York Man never begins to Cut Ice until he is west of Rahway.
1900		Flynt & Walton Powers That Prey 259: I used to be a great bloke for style, but style don’t cut no ice with me any more.
1908		‘O. Henry’ ‘Hostages to Momus’ in Gentle Grafter (1915) 206: That colonel [...] cuts more ice when he goes to the post-office than Roosevelt does when he cleans ’em out.
1911		‘Sing Sing No. 57,700’ My View on Books in N.Y. Times Mag. 30 Apr. 5/3: Whilomville Stories [...] Nix on this. It’s too kiddish and cuts no ice with yours truly.
1917		A. Conan Doyle His Last Bow in Baring-Gould (1968) II 798: It cuts no ice with a British copper to tell him you’re an American citizen.
1924		‘Sapper’ Third Round 640: Me dear old man [...] it cuts no ice.
1937		P. Cheyney Dames Don’t Care (1960) 91: The fact that he tried to commit suicide before don’t cut any ice.
1946		Mezzrow & Wolfe Really the Blues 230: Boasting doesn’t cut any ice.
1953		J. Thompson Savage Night (1991) 143: Excuses didn’t cut any ice with The Man.
1965		J. Orton Loot Act II: That may make a difference to Divine Providence, but it cuts no ice with me.
1975		E. Torres Carlito’s Way 33: That don’t cut no ice ’round heah.
1983		J. Sullivan ‘Yesterday Never Comes’ Only Fools and Horses [TV script] But it’s not going to cut any ice with Arthur Negus’s youngest in there, is it?
1999		Guardian Guide 29 May–4 June 13: Neither does kudos among the actual punters seem to cut much ice.
2000		Indep. Rev. 28 Jan. 14: He’ll maybe tell you you’re pretty which, on its own, doesn’t cut much ice.

2. to chat, to converse.

1902

‘Hugh McHugh’ It’s Up to You 24: Papa used to float in the parlor and cut ice for hours at a time.