07-11-2013 02:14 PM
Hello bcutrone and welcome to the community!
If you are looking to add rigid foam board on top of the drywall I would recommend against it for several reasons. First off, it is against code in most if not all cities because the foam is flammable and once it ignites it gives off a toxic smoke.
In order to add foam board in your closet you would still have to add drywall on top of it. Have you considered adding blown-in insulation. You purchase the insulating at Home Depot and rent the machine (usually free when buy the insulation). Follow the link below on how to install.
Throw off those chains of reason, and your prison disappears