Yes, the above assumption is correct. The winter month, also known as 冬月 (dōng yuè), is the eleventh month of the lunar calendar.
So, It is the month of the winter solstice, the shortest day of the year in the Northern Hemisphere. This makes sense because the lunar calendar is based on the cycles of the moon, which has an average period of 29.5 days.
The winter solstice occurs about every 365.24 days, which is slightly longer than the lunar cycle. To keep the lunar calendar in sync with the solar year, an extra month, called a leap month, is added occasionally.