cut ice

[cut ice] {v. phr.}, {informal} To make a difference; make an impression; be accepted as important. - Usually used in negative, interrogative, or conditional sentences.

When Frank had found a movie he liked, what others said cut no ice with him.

Jones is democratic; a man's money or importance never cuts any ice with him.

Does comfort cut any ice with you?

I don't know if beauty in a woman cuts any ice with him.