1In a food processor combine 1 cup of the gingersnap crumbs, the powdered sugar, sweetened condensed milk, molasses, vanilla, and cinnamon. Cover and process until well combined. Transfer to a bowl; stir in remaining gingersnap crumbs. Cover and chill for 1 hour or until dough is easy to handle.
2Line an extra-large baking sheet with waxed paper; set aside. Using a rounded teaspoonful of dough, shape dough into a 1x1/2-inch log. Place on prepared baking sheet. Repeat with the remaining dough.
3In small saucepan cook and stir white chocolate over low heat until chocolate melts. Add frosting; heat and stir until mixture is smooth. Using a fork, dip logs, one at a time, into white chocolate mixture, allowing excess to drip off. Return to waxed paper. Sprinkle logs with red decorative sugar. Let stand about 30 minutes or until set.
Layer logs between sheets of waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months.