Sift flour, baking powder, and 1/2 teaspoon salt into a bowl. Beat butter and granulated sugar with a mixer on medium speed until pale and fluffy. Beat in eggs and vanilla. Reduce speed to low. Add flour mixture, and beat until combined. Divide dough in half. Shape each piece into a disk, and wrap each in plastic wrap. Refrigerate until firm, at least 1 hour.
Preheat oven to 325 degrees. Let dough stand at room temperature until soft enough to roll out, about 10 minutes. Roll out dough to a 1/4-inch thickness on a lightly floured surface. Add more flour if needed to prevent dough from sticking. Cut out animal shapes using cookie cutters (macys.com), and transfer to parchment-lined baking sheets. Freeze until very firm, about 15 minutes.
Bake cookies, rotating sheets halfway through, until edges just begin to brown, 15 to 18 minutes. Transfer to wire racks, and let cool completely.
Transfer royal icing to a pastry bag fitted with a small plain round tip. Pipe desired designs onto cookies, and immediately sprinkle with sanding sugars. Shake off excess, and let stand until set, about 3 hours.
Decorated cookies can be stored at room temperature for up to 1 week.