In fact, it's precisely the "coldness" of the Jedi's approach that alienates Anakin. "Trust your feelings" has gotten Disneyfied, but it's based on taoist ideas that are perfectly in accord with a clear-eyed apprehension.
It's easy to project various meanings onto SW's use of "feelings," to mix it up with emotion-driven reasoning. But note that this "getting carried away with your emotions" is
precisely what leads people down the path to the dark side. Clearly "trust your feelings" =/= "follow your emotions."
The best way I can explain it is that "listen to your feelings" is about situational awareness and not overthinking your response. It's about letting that response it flow naturally from your context sensitivity. Think of it like Gary Klein's research into firefighter intuition, e.g. this case study:
It is a simple house fire in a one-story house in a residential neighborhood. The fire is in the back, in the kitchen area. The lieutenant leads his hose crew into the building, to the back, to spray water on the fire, but the fire just roars back at them. “Odd,” he thinks. The water should have more of an impact. They try dousing it again, and get the same results. They retreat a few steps to regroup. Then the lieutenant starts to feel as if something is not right. He doesn’t have any clues; he just doesn’t feel right about being in that house, so he orders his men out of the building—a perfectly standard building with nothing out of the ordinary. As soon as his men leave the building, the floor where they had been standing collapses. Had they still been inside, they would have plunged into the fire below.
What happens with the "bad" kind of "feelings"-driven acting and reasoning is that it's fundamentally
desire-driven. The emotional needs and desires and fears of the individual cloud his judgment.
This "feelings vs cold rationality" framing of op exactly misses the point, which is that there's a detached, non-verbal way of using perception and the experience intuition without their being mucked up by emotions. "Cold [verbal, explicit, logical] Spock rationality" and "associative emotional reasoning" are both impoverished ways of operating in the world (see e.g. Bourdieu on habitus, or William James in Principles of Psychology, or the associationist school more generally, for why logical/verbal reasoning falls short—why we need and constantly employ associative intuition). The Jedi philosophy of force usage is "best of both worlds" in what is usually seen as a System 1 vs System 2 tradeoff.