What's the right approach for insulating the slab & footings underneath a masonry fireplace/heater?
If this will be used as a serious heating appliance, (I'm inferring from "masonry heater") not merely decoration (as many fireplaces are), I'd go with uninsulated footing, especially if the stemwall is insulated - whatever thermal bridging takes place will be to the "bubble" of dirt inside the stemwall, which can play into your thermal mass. 

http://www.greenbuildingadvisor.com/blogs/dept/musings/foam-under-footings suggests both that it should be entirely feasible to place foam under, and that it may require negotiations with the LAHJ for code/inspection purposes.