A cold warrior was a person who supported or otherwise participated in a cold war; specifically, one who considered someone from a rival entity with mistrust, and various forms of hostility short of violence.
During the dinner hosted aboard the USS Enterprise-A on behalf of Klingon Chancellor Gorkon, his Chief of Staff, General Chang asked Captain James T. Kirk if he would be "willing to give up Starfleet," following planned easing of hostilities between the Klingon Empire and Federation following the destruction of Praxis. When Spock interjected on Kirk's behalf, pointing out how "the captain feels that Starfleet's mission has always been one of peace," Kirk, continued, "Far be it for me to dispute my first officer. Starfleet has always been..." before Chang interrupted, telling him, "[..] there's no need to mince words. In space, all warriors are cold warriors." (Star Trek VI: The Undiscovered Country)
When Captain Benjamin Sisko attempted to persuade Romulan Senator Vreenak into side with the Federation during the Dominion War in 2374, he used an example of the Federation's lack of experience in replicating Romulan beverages as something "that would change if we became allies instead of cold warriors." (DS9: "In the Pale Moonlight")