ink-painting New Year event
A folk custom held during Koshōgatsu (Little New Year) in the San'in region, where young people paint each other's faces with sumi ink or soot.
See also: 小正月
Sumitsuke-shōgatsu is a traditional event held during Little New Year in the San'in region.
During Sumitsuke-shōgatsu, young people paint each other's cheeks with ink.
Koshōgatsu is the broader Little New Year period (around January 15th), while 墨付け正月 is a specific event within it.
Compound of 墨付け (sumitsuke, 'ink application') + 正月 (shōgatsu, 'New Year'). The name directly describes the custom of applying ink during the New Year season.