Cream butter in a medium mixing bowl; gradually add sugar, beating until light and fluffy. Add eggs and rose water, beating well.
Sift together flour and nutmeg; add to creamed mixture, stirring until well blended. Chill dough at least 1 hour.
Shape dough into 1 1/2-inch balls; roll each ball into an 8- inch rope. Shape each rope into a coil, and place 2 inches apart on greased cookie sheets. Bake at 350° for 12 to 15 minutes. Cool slightly on cookie sheets. Remove from cookie sheets, and cool completely on wire racks.