Mix cookie crumbs, sugar and butter. Press evenly in bottom and up side of ungreased pie plate, 9x1 1/2 inches.
Place marshmallows and milk in large microwavable bowl. Microwave uncovered on High about 3 minutes, stirring once, until marshmallows are melted. Refrigerate about 25 minutes or until mixture mounds slightly when dropped from a spoon.
Beat whipping cream, food color and peppermint extract in chilled medium bowl with electric mixer on high speed until stiff. Stir marshmallow mixture until blended; fold into whipped cream. Fold in crushed candies. Mound mixture into crust. Cover and freeze about 5 hours or until frozen. Cover and freeze any remaining pie.