1. Place cookies in the bowl of a food processor. Cover and process until finely ground (you should have about 3 cups). Add the cream cheese and ginger. Cover and process until dough comes together into a ball.
2. Roll three-quarters of dough into 15 balls and remaining dough into 15 smaller balls. Stack a small ball on top of each larger one. Chill for 1 hour. Insert a lollipop stick into each snowman. Chill 10 minutes more.
3. Place candy coating in a medium microwave-safe bowl. Microwave at 30 second intervals, stirring in between, until melted.
4. Working in small batches, dip snowmen into melted coating, spooning coating over and allowing excess to drip off. Poke the ends of the lollipop sticks into floral foam, styrofoam, or an upside-down shoebox to suspend the pops until the chocolate is set. Chill 10 minutes.
5. Use the remaining melted candy coating to attach a licorice lace scarf and mini marshmallow hats banded with black decorating frosting. Insert a candy-coated sunflower seed for a nose, and pipe on black eyes and buttons. Chill until serving.