This is a great opportunity to insulate your house effectively. Insulating walls can be a laborious and expensive project, but if you need to change the siding anyway, insulation is an easy add-on. If you do not know what is in between the walls, simply drill a hole and find out. In the end the hole will not matter because you will be covering it with the siding. If the house is about 30 years old, when you punch a hole through the wall you will likely find the space between the walls filled with fiberglass. If it is not, then this is the first thing that you should do. After you have sealed the hole, apply 2.5 cm (1 in.) thick sheets of rigid foam insulation over the stucco exterior walls. Over that install the vinyl siding. You will then have a double layer of insulation that can definitely end up reducing your heating costs.