Hogswatch is the festival celebrating the winter solstice and the New Year across much of the Main continent and some other areas of Discworld. It falls on the 36th of December, the new year beginning on the 1st of Ick. It includes elements resembling the Roundworld Christmas traditions as well, especially the Hogfather - a sort of scary version of Santa Claus with added tusks who wears red and white to signify blood on snow. He drives a sled drawn by wild boars rather than reindeer. He is the recent version of an ancient winter god associated with pig-killing and recalls prehistoric pagan kingmaking rituals when smart little bald men would palm a hard bean into the dish of the man they believed would make a good leader for a time (and when winter isn't defeated and the little old bald men sharpen the knives for a sacrificial victim - who better than the new king who isn't helping?).
Many Roundworld traditions have their counterpart on Discworld: carol singing, presents, warm alcoholic drinks, giant department stores with grottoes - even a Wenceslas-type king/peasant scenario that Death and Albert quickly reverse.
Another Hogswatch tradition is that Witches must not go out that night. Like other rules, this one is observed at the discretion of the Witch. The festival features most prominently in Hogfather, and was actually first mentioned in the pre-Discworld novel The Dark Side of the Sun. It is mentioned that the origins of Hogswatch occurred during winter,when a kind king was passing a cottage and heard 3 sisters weeping over having no food to eat. The king took pity and threw a bag of sausages at them (knocking out one of them, but no-one cares).
Image by Matt Smith.