We have found a beautiful 1947 home we are considering buying to downsize from our present 1993 stud wall home. Quite a difference in construction! We have always tried to be energy efficient in our homes. We were amazed at how COLD the walls were during the walk through. The attic revealed large masonary bricks--?4X6 or 8, with brick veneer exterior and plaster interior walls. We live in Southern Ill. Cold winters--0-30's, hot summers--90-100's. So.. we are wondering the best solution to insulate over all the exterior walls of the home, over the plaster, minimizing taking up room space. My husband would be able to do most of the work.
What he would like to do is glue foam board over the plaster walls, screwing down sheetrock instead of adding interior stud walls. Is the foam board going to add enough insulation to be worth all the trouble? And can the sheetrock be screwed to the masonary walls?

Foam board will only get you R.4-8 depending on the thickness but it's at least some improvement. If there is a cavity between the walls, you may be able to blow in or foam some insulating material but unless it is 3" or more you will not get much return for you $$. Rather than screwing the drywall to the masonry walls, he should nail/screw sleepers on the walls, glue the foam in the sleeper spacings and then screw the drywall to the sleepers. Much, much easier than screwing into the masonry. Make sure to use adhesive designed for foam. Google "insulating basment walls" for suggestions since they are almost always masonry. Make sure you have R-30+ in the attic, that's very critical.