This is a somewhat tangential aspect of the question, but interesting nonetheless: at the time of the Korean War, US nuclear law was such that the military could not have access to fully-assembled nuclear weapons without explicit authorization from the President. That is, they were allowed to have the non-nuclear assemblies (the ballistic casing, the fuzing and firing circuitry, the high explosives), but not the nuclear "pits" that were necessary to make them atomic bombs (plutonium or high-enriched uranium). The pits were in the physical possession of the civilian Atomic Energy Commission and the AEC was authorized to shoot (!) any military members who tried to access them without a Presidential order.

But to quote myself:

In April 1951, Truman authorized — without consulting the AEC first — the transfer of a small number of complete nuclear weapons to the military, to be stationed in Guam. By September 1952, Truman had agreed to a proposal that stated that the President still had total authority over when and how atomic weapons could be used, that the DOD would have “custodial responsibility” for all bombs kept outside of the continent US and any that were needed inside of the US, and that the AEC would retain custody for any other bombs.

So the Korean War period was actually the first time that that the President authorized the military to come into full possession of atomic bombs, and they were to be stationed in the Pacific Theatre (Guam).

Which to me indicates that Truman did keep some possibility open for using nukes in that general area. It is hard to imagine any other reason for him to allow the DOD to have nukes stationed there at that specific time. (The Soviets were nuclear-armed, but just barely; it was not about deterrence.)

If you are curious about the interesting history behind how the military was allowed to get full access to nukes, gradually, click on my link above. It is known as the "custody dispute" over the bomb:

The issue in a nutshell: When Eisenhower took office in 1953, there were around 1,000 nuclear bombs in the US nuclear arsenal and all but a few dozen were in the hands of the civilian Atomic Energy Commission (AEC). When he left office in 1961, the nuclear stockpile contains some 18,000 weapons (of widely varying size, yield, and delivery mechanism), and 90% of them were under military control. That shifting of control — of whether it was a civilian or a military organization that physically had responsibility over the bombs — was the essence of the custody dispute.

The US kept the option on the table throughout the war, and both Truman and Eisenhower threatened their use, but there were several factors that delayed the deployment of nuclear weapons, and ultimately, dissuaded US leadership from it.

The war repeatedly swayed from the brink of disaster to near complete victory as the front moved back and forth across the Korean peninsula. The US military was considerably unprepared for the conflict, underestimating the weapons and training of the enemy. The military had undergone deep budget cuts that brought expenditures in 1950 to about 1/7 of what they were in 1945, adjusted for inflation. Training standards for volunteers had fallen. The Strategic Air Command, which was tasked with delivering nuclear payloads to the USSR in the event of war, couldn't get over half its bombers off the ground in a test. Prior to the Korean War, it was believed that making nuclear weapons the central pillar of US defense strategy would be a cheaper and more effective means of deterring and waging wars (Patrick Coffey, American Arsenal: A Century of Weapon Technology and Strategy, page 176). Anticipating their use, 10 bombs were flown to Guam where they were in bomber range of Korea (though one transport crashed and only 9 bombs made it). Still, use of nuclear weapons was delayed because the leadership believed that conventional force alone would be sufficient to win the war, particularly with ample air power. Bruce Cumings in his history of the Korean War notes that more explosive tonnage was dropped over the course of the war than in the entirety of WWII's Pacific campaign.

Truman's chief concern with using nuclear weapons was that it would only further escalate and expand the war rather than end it, and instead increasingly sought a ceasefire rather than total victory. Truman said that while the use of the bomb in 1945 was a necessity to "end the unnecessary slaughter on both sides," Korea was "entirely different." (Daniel Calingaert, Nuclear weapons and the Korean War, Volume 11, Issue 2, 1988) The USSR was already funneling money and weapons to North Korea, and China had become directly involved with the deployment of ground troops. Further, the war was already incredibly unpopular stateside, and Truman has the dubious honor of achieving the lowest approval rating in American history at 22%. (Update: Bush took the title as of Oct 2008 at 19% - thanks frezik) One of the reasons for MacArthur's dismissal was his insubordination in regards to Truman's desire to reach a ceasefire. MacArthur wrote about his opposition to the Republican House minority leader, saying that "there is no substitute for victory." The letter was then entered into Congressional Record (Coffey, page 182).

A comprehensive report outlining potential measures to end the war investigated potential outcomes of nuclear deployment. This report, titled NSC 147, noted that while nuclear weapons may dislodge the enemy and allow for a quicker end to the war, it would make their use be seen as a key component of US military strategy. And, if they failed to bring about a victory, their utility in bringing a decisive end to a conflict would also be called into question. It argued that the USSR may also be deterred from entering the conflict if the US showed its willingness to use the bomb, but spoke little of Communist response except to say that it would depend on how much damage was inflicted. However, though the UN resolution regarding North Korean aggression stated that the UN would "furnish such assistance to the Republic of Korea as may be necessary to repel the armed attack," (UN Resolution 83, it was unanimously believed that use of nuclear weapons would have serious international implications at a time when the US sought to pull the world to its side. Such a decision would only serve to demonize the US in the eyes of the world, marginalize the peace-keeping abilities of the UN, and serve as a poor and dangerous example to NATO allies (Nina Tannenwald, The Nuclear Taboo: The United States and the Non-Use of Nuclear Weapons , page 145-146).

In my opinion then, there are some lasting implications of the bomb's nonuse in the Korean War. Proxy wars were to be kept as such - US leadership was convinced that they should endeavor to prevent them from spiraling into a larger regional or world conflict. Unconditional surrender and total victory were adopted during WWII, but that could not and should not be uniformly considered a reasonable or practical goal for proxy wars. Nuclear capability also could no longer be seen as entirely replacing traditional military might, but would be supplementary (though Eisenhower later made nuclear weapons a centerpiece of military strategy against the USSR in the event of direct conflict, Tannenwald, 175). Finally, nuclear weapons became not merely another tool for waging war, but a distinct weapon with significant domestic and international political repercussions to be used only in specific and dire circumstances.