Cold-eye is a phrase that is often used to describe someone who is giving a stern and unfeeling look or expression. There are several other phrases and synonyms that can be used to convey a similar meaning. Some examples of these words include stony-faced, unemotional, impassive, or expressionless. Other similar phrases could include giving someone the cold shoulder or a frosty reception. The use of these synonyms allows for a more descriptive and varied vocabulary and helps to convey a more nuanced understanding of the situation at hand. Regardless of the specific word or phrase used, the underlying sentiment remains the same: a sense of detachment and a lack of warmth or empathy.