There are quite a few tricks with rendering textures to minimize their impact, I don't remember the name of the technique but it used to be the most common one, it goes like this: you don't actually see the details in the texture until you get close to the object, if you are observant in some old games, you can actually see more detailed textures pop-in as you get closer and pop-out as you go farther.
The mirror would never use the detailed textures since the camera won't get close them, effectively saving on resources, it would often render together with its attached room, just using less detailed objects, but you wouldn't notice cause the tricks of the camera.
This one fell out of fashion cause it can't really be done seamlessly with the hyper realistic graphics of today.
Another technique is to just make a smaller version of the room, and use optical illusions to make it seen exactly as the one you are on.
Both are far easier than programming a mirror.