Probably not all-out nuclear war, actually.
The US stockpile in 1950 apparently had just 77MT combined, rising to just 103MT by 1951. The Soviets, on the other hand, had barely any nukes in 1950/1951, due to inefficiencies in production (since they rushed to get their first nuke tested in '49).
On the other hand, Manchuria (of course, given the OP) and Germany (due to 'better dead than Red' and the need to at least try to stop the Soviets before they can conquer France) definitely eat nukes, along with some major Soviet and Chinese cities. Further, strategic bombing raids by both sides will devastate major cities in Europe, North America, and Russia; the East will generally be hit harder, due to inferior aircraft, but the West will still take some hard knocks. Lots of ugly conventional warfare, too; Germany, Korea (duh), the Low Countries, Greece, Turkey, France and Iberia all get to see a brutal hot war, along with possibly Manchuria, Quemoy, Matsu, and maybe even parts of the coastline of China.
I don't see the Soviets not reacting in some way - if the US feels confident about using its nuclear arsenal against China, then the Soviets have to react or the US will attempt atomic rollback.