Winterfest is an event that celebrates Christmas and other winter holidays. It is used in reference to those holidays.
Every day during Winterfest, one of the Puppet Master's scouts tries to sneak into Lamplight Town, by disguising themselves as a snowman. These may vary in monsters. Find the snowman and defeat the monster inside. If you do, you'll collect a bunch of Magic Snowflakes! You get 10 magic snowflakes to be exact.