http://en.wikipedia.org/wiki/Windows_Mobile
but, yeah that's not really windows for most people.
Also, even if MS ported Windows to ARM (it shouldn't be that difficult), the problem would really be the applications, which would either need emulating (on an already slowish computer) or recompiling.
...well, it does. The kernel does, and so do the desktop environments. And indeed so do most of the applications. But there is no Flash, no Skype, upgrading is a nightmare, support will probably end early and you will be very lucky if Java works well.
Every sub notebook and portable device I owned before my current (Atom based) Eee 1000 was a disaster because the system images for them were universally junk and/or crippled.
The default Linux image for the Eee is _also_ junk, but it doesn't matter because it takes five minutes to throw Ubuntu onto one. This should remain the case for at least the next two to four years as, being standard hardware, new software will keep on being made available for it.
By comparison mainstream support for running Linux on my G4 PowerBook never really began.
I thought the reason was that Windows doesn't run on ARM.