Technically Ded Moroz is created as answer to Santa in 19th century on basis of old pagan winter deity/spirit Moroz/Morozko, and he just lives "in the forest". He wasn't friendly or evil, and acted like typical chtonic spirit, but modern image is mostly Santa-like, with required attributes like bag of gifts and spruce tree.
People rarely care about it though. But most of NY/Christmas items now are about Santa, red hats everywhere (Ded Moroz has blue clothes and different hat), blue are rare. Although reindeer symbolics are rare, only in small gifts (Ded Moroz also has no reindeers) and no chimney with socks - gifts are placed strictly under tree (or just given to person directly of course). People don't care about it either, although purists notice this every year with rants about "Santaization" of NY.