If nuclear weapons were never made, I think that WWIII would've definitely have occurred. I also think America would have to be militarised far more, so it's likely the generals who would've had significant power would've pushed it to a more fascist-style dictatorship. I think the Soviets would've "won" by which I mean taking more territory than the Americans, but it's hard to see an end point to the war. The Soviets and allies would've overrun Europe, the Vietnamese and Thais would have a stalemate, South Korea would be defeated, Japan would be hard to take, the Kurils and Sakhalin would be occupied by the USA. The UK stays on the Allied side, harassing the Soviets. NATO conquers Nicaragua and Cuba. South Africa would conquer Zimbabwe, Mozambique and Angola, but with lots of costly guerrilla activity. The Soviets would have a far bigger advantage if the Sino-Soviet split never happened.