But surely the desktop always has a pointer, so why would it disappear with a new screen?
I'm not really into the fundamentals of OpenGL/DirectX/Windows/whatever. The Desktop pointer however is also a software pointer (that is one drawn manually by Windows) providing the graphics card doesn't support it in hardware.In this case, I would assume, that since Windows is no longer calling the shots, it would stand to reason that the pointer Windows renders, is no longer being drawn. It sounds pretty reasonable.
If you have a rather old gfx card (Riva TNT, early GeForce, anything worse) you can test it by chosing a set of pointers with lots of colors in them. Since the gfx card in question is only likely to have one or two bitplanes, Windows will switch to a software pointer, which will most likely a) disappear when switching to an OpenGL/Direct3D screen, or b) be replaced by the old, less colorful pointer.