On New Year's Eve, children are looking forward to visiting Santa Claus and his granddaughter Snegurochka. It is logical to assume that since Santa Claus has a granddaughter, it means that there must be children and a wife, but in New Year's tales nothing is said about his wife, sons and daughters.
The Snow Maiden became the granddaughter of Santa Claus not so long ago - at the turn of the 19th and 20th centuries, when she began to appear as such at children's Christmas holidays. She became a granddaughter only because Frost himself is called Santa. Initially, the epithet is associated not with the presence of a granddaughter, but with the fact that Frost appears in the image of an old man: white is inherent not only in snow, but also in gray hair, and the earth exhausts its strength by winter, like a person to old age.
But even if we assume that the Snow Maiden is not a granddaughter, but the daughter of Santa Claus, the question about her mother and his wife still remains open.
Folklore tradition
Both Santa Claus and Snow Maiden are present in Russian folklore, but they are not relatives. Folklore Santa Claus bears little resemblance to that kind grandfather with a bag of gifts that comes to children on New Year's holidays - this is the embodiment of a formidable natural element.
A meeting with this pagan deity is not a holiday for a person, but a severe ordeal, which you may not even survive, as happened with the old woman's daughter in the fairy tale "Frost". He gives gifts only to those who have demonstrated their best qualities - like an old man's daughter in the same fairy tale or a needlewoman in the fairy tale "Moroz Ivanovich". Folk tales do not mention any companions or relatives of Santa Claus.
The Snow Maiden also exists in Russian folklore, but she is not associated with Santa Claus. The fabulous Snow Maiden is a girl who is molded out of snow and revived by an old man and an old woman who grieve about their childlessness. The snow daughter feels good in winter, but she is sad in spring, and in summer she dies jumping over the Kupala bonfire. There is no Santa Claus in this tale.
Russian literature
For the first time, the Snow Maiden was connected by kinship with Santa Claus not in the Slavic folk tradition, but in Russian classical literature. This was done by the outstanding writer-playwright Alexander Ostrovsky (1823-1886).
In 1873, the writer was commissioned to play for an extravaganza performance, in which opera singers and a ballet troupe would participate along with dramatic actors. It was then that A. Ostrovsky decided to create a fairy-tale play based on folklore material. He refers to the fairy tale about the Snow Maiden, but retains only the main motive: the child of winter, dying from the heat, the sun, because the plot of the fairy tale is timed not for the New Year or Christmas, but for spring.
In the play by A. Ostrovsky, the Snow Maiden is presented as the daughter of Frost, and the mother of the heroine is Vesna-Red. This connection seems unnatural, that is why the Yarilo-sun is angry, does not give warmth to the country of the Berendeys. Like a folk tale, A. Ostrovsky's play ends tragically: the Snow Maiden melts, but not from the Kupala bonfire, but from the divine fire of love kindled in her heart.
Thus, the only heroine who can be called the mother of the Snow Maiden and the wife of Santa Claus is Vesna-Red. Neither folklore nor Russian literature knows any other candidates for this role.