cold as ice vs frigid

cold as ice

adj
  • Very cold. 

frigid

adj
  • Very cold; lacking warmth; icy. 

  • Chilly in manner; lacking affection or zeal; impassive. 

  • Sexually unresponsive, especially of a woman. 

How often have the words cold as ice and frigid occurred in a corpus of books? (source: Google Ngram Viewer )