The phrase "cuts some ice" means to make a positive impression or to have influence. The opposite or antonyms for this phrase can range from being ignored, dismissed, or having no impact. Words such as "irrelevant," "insignificant," "unimportant," and "unimpressive" are antonyms that can be used to describe something or someone who does not cut the ice. Additionally, words like "inconsequential," "insubstantial," and "trivial" can also be used to describe something that has no real impact or importance, and therefore, does not "cut the ice." Overall, these antonyms illustrate the opposite effects of something that does not make a strong impression.