"cold gaze" is a correct and usable phrase in written English.
You can use it to describe the way someone is looking at someone or something. For example, "He fixed her with a cold gaze, as if he were trying to make her uncomfortable."
His mother-in-law turned her cold gaze back to the plant.
These are exempt from that cold gaze that she casts over everyone else's less than perfect actions".
In 2018, Google was the subject of Vestager's cold gaze, receiving multibillion fines for its anti-competitive practices around its Android operating system, its shopping service and Chrome browser.
Your painted pout and cold gaze were, come to think of it, very like the official lips and eyes of Flora, my wayward wife, and your flimsy frock of black silk might have come from her recent wardrobe".
In the title role Cezary Kosinski has a fierce, cold gaze that bores into you eerily when his image is projected big on the wall of the bunker during some of Macbeth's (very abbreviated) soliloquies.
The night after her boyfriend's death, she goes to a holiday party with Lanna, gets drunk, has three-way sex, then, in the gray light of dawn, goes down to the pebbled shore of the Sound of Mull and, hunched against the cold, gazes at a spit of land across the water.
First, there are the Greeks of the Metropolitan Museum of Art, characterized by their stone-cold gazes and their occasional lack of an arm, head or other appendage.
Sydney is already suspect; the loathsome SD-6 director, Sloane Ron Rifkinn), watches her with a cold, avid gaze.
But following the car crash that claimed the lives of his wife and daughter, Hunter was unable to maintain the cold, scientific gaze of his profession.
Although Joe adopts the paternal attitude of a psychological counselor, shots of him eyeing the boy with the cold, predatory gaze of a chicken hawk make you shiver.
