The virtual machine never "sees" the physical hardware directly (for the most part.) It only sees what is presented in the virtual machine settings. In short, the virtual machine's hard drive the VMDK file that you specify in the virtual machine settings (and/or in the VMX file.) But the it is just an OSX file that to the virtual machine looks like a hard drive.
So more correctly, you do NOT run Windows from the external drive, but you can run the virtual machine from the external hard drive. Just create a new virtual machine, but specific the location of the files to be somewhere on the the external hard drive. Click on customize before hitting finish. Then you can specify where you virtual machine is stored. (If you clicked finish alredy, you can just copy or move the virtual machine package file over to the external hard drive. Then click File, Open to add it back to the Virtual Machine Library.) Windows setup will still only "see" one hard drive (whatever you specified in the virtual machine settings.) But that virtual hard drive file (the .vmdk file) is now stored on the external hard drive.
