So, let us go back in time to the year 1973, specifically around October of 1973; the time frame of the Yom Kippur War. In our timeline, the conflict almost became WWIII after the Soviets threatened to intervene on behalf of Egypt after the ceasefire began to break down. After the American Sixth Fleet was deployed and DEFCON 3 was called, Egypt backed down.
However, in this timeline, Egypt refuses to back down and on the 26th of October of 1973, the US Navy's Sixth Fleet and the Soviet Navy's 5th Operational Squadron face off in a naval battle 10 km off the coast of Crete after the Soviets ignore a warning shot and the Americans open fire, thinking the Soviets are preparing to attack. The 5th Operational Squadron retreats, but the Third World War has begun.
As a consequence, the Soviets deploy 10,000 troops to assist Egypt, and the Americans do the same with marines, and the 82nd and 101st Airborne Divisions. However, the Soviets prepare for a fictional military operation called Operation: Red Thunderstorm; a military invasion of Europe. Around the 5th of November (a reference to V for Vendetta, just to make a fun fact), the Soviets launch an amphibious assault on Narvik to catch NATO by surprise. Two days later, the Soviets begin their push into West Germany, take West Berlin and cross the Fulda Gap, the North German Plain and the Czechoslovakian-German border simultaneously, while fighting erupts in Korea, along with Turkey, the Balkans and (for a few days) Crimea.
Then on the 19th of November, NATO obliterates the Soviets with tactical nuclear weapons as they attempt to cross the Rhine River at around 9:15 AM EST. At around 11:23 AM EST, a NATO counterattack is obliterated by the Soviets also responding with tactical nuclear weapons. The next day, and one tactical nuclear exchange in Germany later, President Nixon orders a first strike against strategic locations in Eastern Europe and the USSR itself at around 10:17 AM EST, which is also the same time Britain, France and Israel launch their warheads. The Soviets then retaliate at around 10:18 AM EST. By 1:57 PM EST, the majority of the Northern Hemisphere is obliterated in nuclear fire and radiation, and the war ends with 459 million dead across the globe, and millions more injured.
The problem? Would the Warsaw Pact even get close to the Rhine River? If so, would NATO realistically be able to obliterate them or let Central Europe get overrun? Feel free to provide some answers.
EDIT: I want to tell you as a fun fact that I originally planned the body count to be 970 million, since I originally wanted to drag China into the war, but since they would not have time for that, that idea was scrapped.
Also, to clarify: the 459 million dead is those killed in the initial attacks. I still have yet to develop the aftermath, but I am going to guess billions are going to die afterwards.