FYI there was never a global nuclear holocaust; but people still built nukes. In fact there was never direct fighting between the US and Russia...
>> The American commanders in the field reported that the Czarist reign of terror was far more horrific and disturbing that the actions of the Reds. The American forces also discovered that the vast majority of Russians sympathized with the Bolsheviks and supported the revolution. In the end, the American troops were brought home without any fanfare, and the ordeal was considered one of the most ill-conceived interventions in American history up to that time.
From http://rationalrevolution.net/war/russian_revolution.htm