Hyper-threading has nothing to do with the architectural state of the OS, which exactly what you need to differentiate. While you can use techniques to create virtual processors, the operating systems running on those processors have to at least be in the same family, if not indeed the same OS.
I can't give a definitive answer on this though, as it's something I've never actually tried. I routinely build multi-seat systems with isolated heads for each system, but never tried to do so using different operating systems as a base on a single processor system, hyper-threaded, dual core or otherwise.
My best guess would be that if you ever did get something like this working, it would be unstable at best and fry your processor and possibly any other hardware connected to it at worst. Windows and Linux are two very different operating systems on the kernel level (thank God) and, while a Linux kernel could be made to segregate itself into only a portion of a given processor and to only use dedicated RAM space, I doubt you'll be able to do this with much luck with a Windows kernel. Not being able to do this will mean it'll only be a matter of time before your Windows kernel invades the Linux kernel space causing both systems to crash horrifically.
As I said though, I've never tried it. If you really need to have both operating systems running at the same time, you can get all the hardware you need for a second system and a KVM switch for less than $500.
If you absolutely must do this, best of luck to you.
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