cut ice vs make a difference

cut ice

verb
  • To have influence (on something, especially someone's opinion); to be accepted or tolerated (by). 

make a difference

verb
  • To be of importance; to matter. 

  • To carry out an action, the result of which is a significant change, or an altered circumstance. 

How often have the words cut ice and make a difference occurred in a corpus of books? (source: Google Ngram Viewer )