Where does the custom of winter solstice come from

The following is the origin of the winter solstice custom:

There is a custom of eating mutton on the solstice in winter. According to legend, this diet custom originated in the Han Dynasty. Liu Bang, the Emperor Gaozu of Han Dynasty, ate cooked mutton on the solstice in winter, which was highly respected. Since then, the custom of eating mutton from winter solstice has been formed among the people. Today, some areas still retain this eating custom. Every winter solstice, some areas have ushered in the peak of drinking mutton soup. People think that drinking mutton soup can keep warm and resist the local wet and cold environment.