on thin ice vs out on a limb

on thin ice

adv
  • dangerously, hazardously, delicately 

prep
  • In a dangerous, hazardous, or delicate situation; at risk. 

out on a limb

phrase
  • In a risky, precarious, daring, or uncompromising position, especially one outside of the mainstream; vulnerable. 

How often have the words on thin ice and out on a limb occurred in a corpus of books? (source: Google Ngram Viewer )