In ancient past New Year was celebrated at 1st March, then at 1st September (in 1492), then Peter I changed date to 1st of January in process of westernization. It was celebrated officially, but Christmas, of course, was celebrated too. Image of Grandfather Frost (Ded Moroz) - a pagan chtonic spirit/deity, was changed in late XIX to be like Santa (before he wasn't so friendly and didn't bring any gifts, although can give gifts to good people when encountered). It was typical 19th-century folk-like revival (like all that Germanic thing in Germany, Wagner operas, Nordic imagery etc).
In Soviet times Christmas tradition and New Year were suppressed, but NY then was ressurected in 30s. Ded Moroz and his granddaugher Snegurochka (snow girl) became official symbols of New Year and acted like Santa, but without chimney and deers - they put gifts under spruce. Sometimes, especially in Soviet period, young boy who symbolized new year was used too.
Recently image of Santa and Ded Moroz merged, even the red coat (original was mostly blue). Christmas, on other side, isn't associated to Ded Moroz at all now, it is purely religious holiday, no tree, no gifts, nothing, only some large church vigil translated on some TV channels (no one cares).
Actually, this is one long holiday week, from 1st to 8-10 (depending on year), so both dates are fit in one period when people mostly not work (shops, police and other things are open of course). In this year it is from 1st to 8th. There always talks about splitting this week because it is damaging to economy, but nothing changes.>How's the calendar now? Was Gregorian adopted? I remember that we had to celebrate the Great October Socialist Revolution on Nov 7th and it was the subject of ridicule (not great, not october, not socialist and not revolution).
Russian Orthodox Church still use old calendar, so Christmas happens on 7th January. There is also traditional unofficial holiday called "old New Year" on 13th Jan, it is NY in Julian calendar, and people often celebrate it, but not that seriously as modern NY. At 25th some local catholics celebrate of course.