In a large bowl, with mixer on medium-high, beat butter and sugar until fluffy, about 3 minutes. Beat in egg, corn syrup, and vanilla. Reduce speed to low and beat in flour. Divide dough in half. Shape each dough half into a disk. Cover with plastic wrap and refrigerate 1 hour.

Heat oven to 350 degrees F. Roll dough to a 1/4-inch thickness on a floured surface. Use an assortment of snowflake-shaped cookie cutters to cut out cookies. Transfer to a baking sheet, spacing 1 inch apart. Bake 16 to 20 minutes or until golden. Let cool 1 minute. Transfer cookies to wire rack and let cool completely.

To decorate cookies: In a large bowl, with mixer on low, beat together confectioners' sugar, egg whites, and 3 tablespoons water. Increase speed to high and continue beating until stiff peaks form. With a spoon, stir in remaining 1 tablespoon water. Using tip of index finger, spread icing over cookie. Top with nonpareils or sugar crystals. Let dry completely.