Preheat the oven to 350 F. In a medium bowl, whisk together flour, salt, and baking soda. In a large bowl, mix butter with sugar until fluffy. Add in egg and mint extract and mix until smooth.
Add in the flour mixture and mix until combined. Add in the food coloring. Place powdered sugar into a shallow dish and roll the cookie dough into balls and roll in the powdered sugar.
Place cookies onto a large ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes.