Restricting this to just Soviet Russia for simplicity. First off, Russian Christians followed the Orthodox traditions, which even to the present day still uses the Julian calendar for observing religious celebrations. This puts Christmas on January 7th of the following year (according to the Gregorian calendar). Prior to the creation of the Soviet Union Russians began to celebrate Christmas as a seasonal and religious holiday, a bit as it is done in the West.

During the early years of the USSR Christmas was banned, as was Christianity and all open religious observance, replaced with a policy of state atheism. In 1935 Stalin decided to return some semblance of Christmas to the USSR by pushing the idea of a New Year's celebration using a tree and many of the trappings of modern Christmas (which itself is a bit of a pastiche of different celebrations both religious and secular even though it has been claimed under the banner of Christendom). New Year's trees, and "Fir Tree Decorations" (bearing a strong similarity to traditional Western Christmas decorations) became available, along with guidelines on how to hold a proper New Year's Party.

Starting in 1948 New Year's day became an official "non-working day" in the USSR, and afterward it became an increasingly important holiday and day of celebration, eventually becoming arguably the largest holiday of the year.

Of course, many Russians held onto an adherence to Christianity and its traditions even through the revolution and through the Soviet period. Even after decays of Soviet rule today only a minority of Russian's consider themselves atheist while the vast majority (over 70% by some polls) consider themselves Christian. Under the Soviet Union Russians infused the New Year's celebration with as many of the elements of Russian Orthodox Christmas celebrations as it was possible to get away with. The familiar large family dinner, gifts under a tree decorated with lights, garlands, and glass ornaments (though perhaps topped with a five pointed star of the Red Army rather than the star of Bethlehem or an angel), etc.