Preheat the oven to 350 F. In a large bowl, mix together butter and powdered sugar until fluffy. Add in vanilla extract and mix until smooth. Add in the flour mixture and mix until a thick dough forms. Add in the green food coloring.
Roll the cookie dough into balls and place onto a large ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes. Place powdered sugar into a shallow dish, and roll each one in the sugar.