At work we use "dummy" terminals that you are describing over a Unix Inventory/Point of Sale system. This is very basic in it's data transfer. I would assume that in a Windows environment, the desktop alone would be too much for a dummy terminal. I haven't see this type of setup for windows based machines. The closest to that type of setup that I have encountered is using a metaframe circuit on a Citrix Server. Basically, your controlling a session on a remote server, just transfering keystrokes back and forth between the client and the server. All processing occurs at the server, you just get screen refreshes. Much like how PC Anyware works, but much much better. This still requires minimum 486x processor with Mobo, graphics card, ect....
How far do you have to go?