1. On sheet of waxed paper, sift flour with baking powder, salt and nutmeg; set aside.
2. In large bowl of electric mixer, at high speed, beat butter, sugar, eggs and vanilla until light and fluffy.
3. With wooden spoon, stir in half of flour mixture. Then add rest of flour mixture, mixing with hands if necessary.
4. Refrigerate dough, covered, several hours or overnight.
5. Preheat oven to 400 degrees. Divide dough into four parts; refrigerate until ready to roll out.
6. Between two sheets of waxed paper, on slightly dampened surface, roll out dough, one part at a time, 1/8" thick.
7. With floured cookie cutters, cut out cookies. Place cookies 2 inches apart , on ungreased cookie sheets.
8. Bake 8 minutes, or just until set and lightly browned around the edges. Remove the cookies to wire rack; cool completely.
9. Make frosting. In medium bowl, with electric mixer at medium speed, beat egg whites with sugar and cream of tartar until mixture is stiff enough to hold its shape.
10. Divide icing into five small cups. Add enough food coloring to each bowl to tint desired shades of color. Leave 1 bowl white.
11. Spread cookies evenly with decorating frosting. Store in airtight cookie jar or tin, in a cool, dry place for several weeks.