The Korean War was as much of a verification of the Cold War as anything. Leading up to the Korean War, the Cold War was filled with threats and escalations with limited action, so to speak. However, this new war forced all sides to realize that this "Cold War" wasn't so cold anymore.
The Korean War's most notable impact on the Cold War itself was through nuclear warfare. This was the first time that the United States and the Soviet Union came to the forefront with nuclear weapons. This fact alone set off tensions in the Cold War for the next several decades.
Another element of the Cold War that began in Korea was the idea of proxy wars. Both the United States and the Soviet Union became deeply involved in this fight—but in other third world countries. The influence of communism forced the United States to desperately enter into any country under the Soviet Union's hand.
Finally, one of the least talked about aspects of the Korean and Cold War is the impact on the United States. In the aftermath of Korea, the United States became what we know now as heavily militarized. In today's currency, the US spent in the hundreds of billions in the Korean War and afterwards. The threat of the Red Scare and the expectations of the proxy wars to come created a heavily militarized and defensive country in both the United States and Soviet Union.
The Korean War increased tensions that already existed between the communists and the noncommunists. After World War II, the United States had developed the policy of containment in order to prevent communism from spreading. When China became communist in 1949, the United States feared that more attempts would be made to spread communism elsewhere in Asia. When North Korea invaded South Korea in 1950, this belief was confirmed. The United Nations, led by the United States, took a military stand against this aggression and helped South Korea in its fight to remain free from communist rule. This war showed that both sides were willing to fight for their beliefs.
The Korean War further convinced the United States that had it had to continue to work to stop the spread of communism. This was one reason why the United States later intervened in Indochina and eventually in Vietnam. In World War II, the United States learned that aggressive actions needed to be stopped. The United States felt the same was true when the communists tried to spread their influence to noncommunist regions in Europe and in Asia.
Another impact of the Korean War was that it led to the development of an arms race. Both the United States and the Soviet Union significantly increased the number of atomic weapons that they had. It also led to the development of the space race.
These events allowed distrust and fear to continue to build on both sides. This led to future Cold War conflicts such as the Vietnam War and the Cuban Missile Crisis.
The Korean War was the first major proxy war of the Cold War period. As such, it strained relations between the United States and the Soviet Union to an extreme degree. The Korean War was a serious test of the United States' containment policy. This policy was formulated in the late 1940s with the goal of preventing the spread of communism around the world. By attempting to prevent the Korean Peninsula from falling to a communist regime, the United States and NATO entered into a direct military conflict with allies of the Soviet Union and even certain Soviet military forces. This established a precedent that would be repeated again and again during the Cold War, most notably in Vietnam a decade later.
The Korean War also had a large impact on the relationship between members of NATO, as it was the first major NATO military action. It took what had been a mere political agreement between member nations and strengthened it into an active military alliance.
The war, though long, bloody and costly, also seemed to prove and justify that a policy of containment - stopping the spread of communism to other countries - worked and was justified. This would be part of the reason why we would get involved in Vietnam a short time later. The war was mostly between the US and China, so there were tense relations between our two countries for more than 20 years following the Korean conflict.
It accelerated the Cold War between us and the Soviet Union, as the North relied on Soviet weapons to fight the war, and some Soviet pilots even flew missions against American jets during that time, and we knew it. We accelerated the arms race, and the public became overwhelmingly convinced that the Soviets were bent on world domination, and social hatred of them and communists grew rapidly in the early 1950s.
The major impact of this war was to make the Cold War seem more serious to the US policy makers and to other non-communist countries, especially in Asia.
Because of this war, the US really stepped up its program of containing communism. It increased the number of active duty military personnel in a big way and it started to station more of them at bases around the world.
The US also started to get more serious about trying to help the countries of Asia out economically and militarily. This was when we started to really defend Taiwan and guarantee its security against Mainland China, for example. We also started giving more foreign aid to various countries to keep them on our side.