On a lightly floured surface, roll dough into a 14-in. square. Spread with butter. In a small bowl, combine the brown sugar, walnuts, cinnamon and nutmeg; add apples and toss to coat. Sprinkle over dough to within 1/2 in. of edges.
Roll up jelly-roll style; pinch seam to seal. Cut into 12 slices. Place cut side down in a greased 11x7-in. baking dish. Cover and let rise in a warm place until doubled, about 40 minutes.
Bake at 350° for 25-30 minutes or until golden brown. Combine icing ingredients until smooth; drizzle over warm rolls.