In my opinion, the major impact of the Korean War came because people were simply tired of that war. That helped defeat Adlai Stevenson because he was too connected to President Truman in people's minds.
Because people were tired of the war, they wanted it to be over with. They equated Stevenson with Truman, who had not been able to bring the war to an end. They thought that Eisenhower would be more assertive and would get the war over with one way or another.
Ike helped make people think that by promising to go to Korea if elected -- this made it seem like he had some sort of plan without him having to say what that plan was.
Although Dwight D. Eisenhower might well have won the 1952 election without the Korean War, that war helped him be more certain of victory. The stalemate in the war and Eisenhower’s credibility as a hero from World War II helped to seal his victory.
By 1952, the war in Korea had become a stalemate. As such, it had become rather unpopular in the United States. Eisenhower used the people’s unhappiness over the war to his benefit. One of the major themes of his campaign was that the Democrats had mishandled the war. He charged that the Democrats had not been sufficiently prepared for a war. Because of that, he said, the war had ended up in a stalemate. He had credibility on such issues because of WWII. He promised to find a way to end the war if elected. This, too, helped make him more popular.
With Ike’s popularity, it is possible that he would have won the election regardless. The war in Korea, however, helped to make him more popular and thereby helped to ensure his victory in 1952.