Santa Claus isn't the only Christmas character who brings gifts. There's a wide number of different gift-bringers in cultures across the world, and a significant portion of them are ladies.
As far as I can find out, the first mentions of a Mrs. Claus go back to the mid-18th century. In the 1849 short story The Christmas Legend by James Rees a couple disguises themselves as "old Santa Claus and his wife." Then in 1851, in The Yale Literary Magazine, one author remarked that Santa "we should think, had Mrs. Santa Claus to help him." From there, the floodgates opened. Mrs. Claus appeared all over the place in short stories and poems, helping Santa Claus with his work.
Some of her other names are Mother Christmas (English), Weihnachtsfrau, Nicolaaswijf (German), Joulumuori, Kerstwrouvtje, Kerstomaatje (Finnish), Bayan Noel (Turkish), or La Mère Noël (French). She never really got a name beyond "Santa's wife" in any of these languages - although in a March 1881 issue of Harper's New Monthly Magazine, we learn that among Dutch immigrants, St. NIcholas was "sometimes accompanied by his good natured vrouw, Molly Grietje." I have yet to find other textual support for this tradition, and this may not be a factual account of Dutch settlers.
In other countries, St. Nicholas was occasionally accompanied by a female counterpart, like the Niglofrau (Nicholas wife) in Upper Austria and the Nikoloweibl in Bavaria. (The Krampus and the Old, Dark Christmas). In Tirol, there was the Klasa (a feminine variant of Klaus), a well-dressed woman who went in St. Nicholas's processions and distributed gifts from her basket. This was recorded in 1875 in Tagespost Graz. A Friesian nursery rhyme, published in Dutch in 1892, implied the existence of a whole Santa family, with Sintele Zij as the wife.
But female gift-bringers of Christmas go back further. In some cases, a female saint appeared in place of Saint Nicholas. One of the most famous was Saint Lucy, whose feast day falls on December 13. In Sweden, there were Lucia processions where she led a troop of children dressed in white, including the stjärngossar or star boys.
In the Czechlands, on December 4 - the eve of St. Barbara's Day - women would dress as the Barborky, or Barbaras, in white dresses with veiled faces. They carried baskets of fruit and sweets for the good children, and brooms to threaten bad children. (Czech Traditions and Folklore) (Prague City Line)
In some Czech families that immigrated to America, Matíčka or the Blessed Mother would leave treats in children's shoes on the Feast of the Immaculate Conception (December 8). (Christmas in Texas)
In a lot of Christian countries, people cut out the middleman and had Baby Jesus bring gifts. However, somehow this got turned around. The German Christkind became America's Kris Kringle, alias of Santa Claus - and in Germany, became a beautiful young girl like Lucia, dressed in gold with a crown on her head. The same thing happened to the Wienechts-Chindli in Switzerland and the Kinken Jes in Sweden. There was also the Wends' veiled Dźěćetko (Little Child) or Bože dźěćo (God’s Child).
In other countries, the gift-bringer was an elderly crone like the Befana (Italy), Babushka (Russia), or la Vieja Belén (Dominican Republic). Searching for the Child Jesus, she gives gifts to the children she meets along the way.
These Christian characters replaced older figures from older winter festivals. For instance, the Christian martyr Lucy stepped into the shoes of an older figure, the terrifying Lussi. These gift-bringers varied from beautiful, shining young women to monstrous hags. They often made their visits between Christmas and the feast of Epiphany.
Perchta, Frau Holle, Hulda, Frau Gode, Frau Lutz, Bertha, Butzenbercht, or Eisenberta (Iron Berta) were some of the many names used for a Germanic goddess figure. Traveling with her assistants, she would bless the people who welcomed her into their homes in the twelve days between Christmas and the feast of Epiphany. She passed judgement on those whose work didn't measure up. According to the Thesaurus pauperum (1486), between Christmas and Epiphany, people left out food and drink at night for a woman named Lady Abundia, Domine Habundie, or Satia. Dame Abonde was apparently still around in the 19th century as a French gift-bringer of New Year, according to Brewer's Dictionary of Phrase and Fable (1898). Names like Frau Faste and Quatemberca referred to the Ember Days.
In some cases, the Perchta character was a hideous monster well-known for her one goose foot and her long beak-like nose - earning her the Austrian name Schnabelpercht or Beak Perchta. Martin Luther referenced "Dame Hulda with the snout." She was also known as the Spinnsteubenfrau, or Spinning Room Lady. In Franche-Comte, Tante Arie was a gift-bringer but also a frightening figure with iron teeth and goose feet. The chauchevielle (also a name for a bogey or a nightmare) and the trotte-vielle were terrifying figures active around the holly-jolliest of seasons. In Iceland, Gryla was a troll who ate bad children and in modern times gained an association with Christmas. In the 19th century, Jacob Brown wrote of his childhood in Maryland and the Christmas visitor known as Kriskinkle, Beltznickle or the Xmas woman. They were disguised and "generally wore a female garb - hence the name Christmas woman." (Brown's Miscellaneous Writings)
On the softer side, there were beautiful White Lady types. La Dame de Noel showed up in Alsace. Anjanas, in Cantabria, were fairies of the mountain who would bring gifts on January 6 every four years (Manuel Llano, Mitos y leyendas de Cantabria).
So before the beautiful Marys and Lucias, and before the old crones like La Befana, there were already lovely ladies and hideous hags going back to much older myths. These myths surrounded goddesses and demons who were celebrated around the winter solstice. Some of these names, like Bertha and Lucy, have names which intriguingly mean bright or light. St. Lucy, as already mentioned, has "star boys" for companions. In some areas of Poland, the gift bringer was not St. Nicholas, but the Gwiazdor (star man) and sometimes along with him, the Gwiazdka (star woman) or Piękna Pani (beautiful lady). (Star symbolism and Christmas gift-bringers from Polish folklore) Was this related to a celebration of the sun's return and the days growing longer after the winter solstice?
More characters have been created during modern times. Mother Goody, Aunt Nancy or Mother New Year brings gifts for New Year’s in Canada. Snegurochka (Snow Girl) is the young female helper of Ded Moroz (Father Frost) in Russia. (Babica Zima, or Old Woman Winter, may also have been proposed as a gift-bringing figure.)
In a funny twist, during World War II, women sometimes took up the whiskers and played Santa Claus. "Kristine Kringle! Sarah St. Nicholas! Susie Santa Claus!" one scandalized columnist called them. (Smithsonian) One wonders what that writer would have thought of the older tradition of otherworldly women who came at midwinter with gifts and punishments. Leaving out cookie and milk for Santa probably has its origins in the same tradition where people left out offerings for Lady Abundia.
Researching folktales and fairies, with a focus on common tale types.