This modification is so simple it should have been included in the game by default, and has no effect of Multiplayer games whatsoever.
First, if you're using WindowsXP, open an Explorer (not IE) window and on the toolbar, click TOOLS, and then FOLDER OPTIONS. In the window that pops up, click the VIEW tab, and make sure that 'Hide extensions for known file fypes' is unchecked. If it IS checked, clear the box and click OK. One of the reasons that this modification fails to work for some people is with the file we are going to create being saved as Autoexec.lua.txt. Ok, that done on to the next part.
Navigate to your Dawn of War installation directory, in a default installation this is: C:\Program Files\THQ\Dawn of War\
Once there, right click in the folder and select NEW, and then TEXT DOCUMENT. For the moment, leave the name as it is and double click the new text document, and paste the following into it:
screenmode = 0
if screenmode == 0 then
screenmode = 1
screenmode = 0
Close the document, saving on exit. Now, rename this document Autoexec.lua (this is the bit where showing file extensions for known file types is important, otherwise, with the .txt extension hidden, it will more than likely save the document as Autoexec.lua.txt, which will of course cause it to fail to work).
That done, and if all is going according to plan, next time you play Dawn of War (or Winter Assault, and I'm assuming it'll also work with Dark Crusade), pressing SHIFT+TAB during a game or replay will toggle the HUD on or off.