Combine first 3 ingredients in a heavy saucepan. Cook over medium heat, stirring frequently, until mixture comes to a boil and sugar dissolves. Continue cooking, stirring frequently, until mixture reaches soft ball stage (240°).
Beat egg whites (at room temperature) until foamy. While beating at medium speed of electric mixer, slowly pour hot syrup in a thin stream over egg whites. Turn mixer to high speed, and continue beating until stiff peaks form and frosting is thick enough to spread. Fold in marshmallows.