COOKIES: Combine all of the ingredients in a bowl and beat with a hand or stand mixer until well blended. Refrigerate dough for 1 hour. Drop by teaspoonful onto a parchment lined baking sheet. Lightly press with your fingertips to flatten and shape a bit. Bake at 350 degrees for 8-10 minutes.
FROSTING: Stir confectioners' sugar and lemonade mix together in a small bowl. Beat in the butter. Add the milk gradually, until the frosting reaches a spreadable consistency. You want it thick, but smooth enough to spread. Frost cooled cookies and decorate with sprinkles.