Heat oven to 375 degrees F. In large bowl, break up cookie dough; thoroughly work in flour. Work with half of dough at a time, refrigerating remaining dough until needed.
On work surface sprinkled lightly with flour, roll dough 1/4 inch thick. Cut with floured 2 1/2- to 3-inch snowflake-shaped cookie cutters; place 1 inch apart on ungreased cookie sheets. Repeat with remaining dough, rerolling scraps.
Bake 7 to 10 minutes or until cookies are set and edges just begin to brown. Cool 1 minute; remove from cookie sheets to cooling racks. Cool completely, about 10 minutes.
Meanwhile, in medium microwavable bowl, microwave white vanilla baking chips and vegetable oil uncovered on Medium (50%) 1 to 2 minutes, stirring every 30 seconds, until smooth. Spread mixture on cookies, and place close together on sheet of waxed paper or cooking parchment paper. Let set 5 minutes.
Place blue candy melts and creme de menthe chips in separate medium microwavable bowls, and microwave each uncovered on Medium (50%) 1 to 2 minutes, stirring every 30 seconds, until smooth. With 2 small spoons, drizzle candy melts and creme de menthe chips over white chips.