The Celtic festival that marks the beginning of winter and begins on October 31 is Samhain.
Samhain is a Gaelic seasonal festival traditionally observed on 1 November, with celebrations beginning at sunset on 31 October because the Gaelic day began in the evening. It marked the end of the harvest and the start of winter, or the “darker half” of the year. This makes the question’s October 31 date a reference to the festival eve rather than its formal calendar date.
Samhain was one of four major Gaelic seasonal festivals, alongside Imbolc in early February, Bealtaine in early May, and Lughnasadh in early August. Historical traditions included bonfires, feasting, divination, protective rituals, and beliefs that the boundary between the living and supernatural beings was especially permeable.
Halloween developed partly through the Christian calendar’s placement of All Hallows’ Eve on 31 October and later absorbed older seasonal customs. Samhain is therefore related to Halloween, but the two are not simply interchangeable: one is an historic Gaelic festival, while the other became a broader Christian and popular holiday.