beginning of midwinter; start of the coldest season
Refers to the first day of the traditional 寒 (kan) period, around January 5th or 6th, marking the onset of the coldest time of year in the old calendar.
After the beginning of midwinter, the real winter cold sets in.
寒の入り is the beginning of 寒, the cold-season period of the traditional calendar. It falls at 小寒, one of the twenty-four solar terms.