Originally, no, they were first developed in WW2. However development of new and better ones was going on in the Korean War, so yes. And it continues even now, the US tests by simulation on supercomputers, most other countries test underground.
Not during the Korean war...
Nuclear weapons
Nuclear weapons
Nuclear weapons
From Russia and China.
Nuclear weapons developed by the Manhattan project for the Allies were Fission weapons called Atomic bombs. Large scale Fusion weapons developed by Hungarian Edward Teller in USA after WW2 were called Hydrogen Bombs. However during 1942 the Nazis developed a hybrid fusion boosted fission weapon, in which hollow charge explosives were used to cause a plasma pinch, a kind of flash of neutrons to ignite a Fission explosion.
The US chose NOT to deploy nuclear weapons. (The US did deploy nuclear weapons against Japan in WWII). The US chose NOT to invade North Vietnam. (The US did invade North Korea during the Korean War).
Nuclear weapons, Biological Weapons, Chemical Weapons.
The largest policy was that the war would be LIMITED to non-nuclear weapons; for the first time in US history a war would be fought without using the full resources of weapons available (e.g. atomic bombs).
Intimidation
The United States used the atomic bomb offensively during WWII. That is pretty close to nuclear weapons.
The only country that has ever used nuclear weapons in any war was the US, at the end of WW2.