In large bowl, beat 3/4 cup butter and 1/2 cup sugar with electric mixer on medium speed until light and fluffy. Add egg; beat well. Stir in 1 3/4 cups flour, the baking soda, cream of tartar and salt. Knead dough into smooth ball. Wrap in plastic wrap; refrigerate until firm, about 1 hour.
Meanwhile, in small bowl, mix 1/2 cup butter, the milk and 1/2 cup flour with fork until well mixed. Divide mixture in half. Stir red food color into 1 half and green food color into other half. Spoon each mixture into decorating bag fitted with small writing tip; set aside.
Heat oven to 375°F. Shape 1 half of the cookie dough into 3/4-inch balls. Place balls 2 inches apart on ungreased cookie sheets. In small bowl, measure 2 tablespoons sugar. Dip bottom of glass into sugar, and use to flatten each ball into 1 1/2-inch round. Pipe colored mixture from decorating bags on each cookie in various holiday designs. Repeat with remaining half of dough.
Bake 7 to 9 minutes or until set. Immediately remove to cooling rack.