The frosting is more a glaze than a true cream cheese frosting. It will give you a thin layer of cream cheese on the cake.
I don't really care to put cakes in the refrigerator, but since this cake has a cream cheese frosting you may want to. To serve the cake if refrigerated, place the slice of cake in the microwave for 20 -30 seconds to bring the cake to room temperature and enjoy the aroma and taste of it as if you just baked it!