In a large mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add powdered sugar, vanilla, baking powder and salt. Beat till combined, scraping sides of bowl occasionally. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in tangerine peel and any remaining flour. Divide dough in half. If necessary, cover and chill dough 30 minutes or until easy to handle.
On a lightly floured surface, roll half the dough at a time till about 1/4-inch thick. Cut dough into shapes using a 3- to 4-inch snowman-shaped cookie cutter. Place 1 inch apart on ungreased cookie sheets.
Bake in a 350 degree F oven about 12 minutes or till edges are firm and bottoms are very lightly browned. Transfer to a wire rack and let cool. Frost with Powdered Sugar Icing. If you like, while icing is still wet, decorate with small candies for nose and buttons and add Gumdrop Hats and Scarves. Makes about 4 dozen cookies.
In a small bowl combine powdered sugar, vanilla, and milk. Stir in additional milk, 1 teaspoon at a time, until icing reaches desired consistency.