Cream butter in a large mixing bowl; gradually add sugar, beating well. Add eggs, one at a time, beating well after each addition. Stir in vanilla and lemon extract.
Sift together flour, baking powder, salt, and nutmeg in a medium mixing bowl. Gradually add to creamed mixture, stirring well after each addition.
Roll dough to 1/8-inch thickness on a heavily floured surface; cut dough with assorted cookie cutters. Place cookies 2 inches apart on lightly greased cookie sheets. Bake at 350° for 8 minutes. Remove from cookie sheets, and cool on wire racks.