December got its name from the Latin word decem (meaning ten) because it was originally the tenth month of the year in the calendar of Romulus c. 750 BC which began in March.
The winter days following December were not included as part of any month.
The ancient Roman calendar only had ten months in the year, beginning with the month of March. January and February were eventually added after December to the end of the year. But, by the time the Julian calendar was established in 45 bc, January and February appeared at the beginning of the year, which bumped all of the original months (and their originally assigned names) back by two.
Before December entered Old English, the terms for December were Ǣrra Gēolaor Gēolmōnað, meaning “yule month.” The early Germanic people celebrated the mid-wintery season during a time that was called yuletide, a two-month period that spanned December and January. With the rise of Christianity, the yule was condensed and adopted into the liturgical year under the Christian name Christmastide, which begins on Christmas Day and lasts a total of 12 days—the 12 days of Christmas.
Every time Santa is referred to as “jolly,” remember the fact that jolly may have derived from the same Old Norse root that brought us yule.
Even if we no longer call it the “yule month,” the association we have with December is celebrating the Winter Solstice.