Line cookie sheet with waxed paper. In large microwavable bowl, microwave marshmallows and butter uncovered on High about 2 minutes, stirring every 30 seconds, until melted.
Stir in popcorn and snack mix. Grease hands with vegetable oil. For each snowball, shape 1/3 cup mixture into ball. Place balls on cookie sheet to set.
In small microwavable bowl, microwave white chocolate and shortening uncovered on High about 2 minutes, stirring every 30 seconds, until melted. Drizzle over top one-third of each ball to look like snow. Sprinkle with coarse sugar.