Russian Christmas is a holiday that used to be the main Russian winter holiday up until the October Revolution in 1917. When bolsheviks came to power, they decided to eliminate all things religious and ban all church holidays. And that’s why Russian Christmas was not celebrated - and if celebrated, then in strict confidence - for more than seventy years. After the Soviet Union collapsed, Russians quickly restored traditions of Russian Christmas and other religious holidays.
Russian Christmas is celebrated on January 7. Orthodox Christians try to follow a forty day fast, which ends the night on January 6, when they go to the church to attend the Christmas service, which usually ends way past the midnight.
If you want to congratulate someone on Russian Christmas, you have three options. You can say “S Rozhdestvom!”, which stands for “Merry Christmas!”. Or you can go for “S Rozhdestvom Khristovym!”, which is “Happy Birth of Christ!”, or — use “Schastlivogo Rozhdestva!”, which means “Happy Christmas!”.