***DISCLAIMER*** I have not tested this method my self, therefore I highly recommend that you backup your internal hard drive to prevent data loss and continue at your own risk ***DISCLAIMER***
To install Windows to an external hard drive using VirtualBox you may use the following as a guide.
To create a Virtualbox 'RAW disk VMDK' to attach a physical drive to a virtual machine you will first need to have VirtualBox installed of course.
Next open Disk Utility with your desired disk attached and find the BSD device node of the drive by looking in the drives 'Info' window and looking for something like 'disk1' or '/dev/disk1'.
Once you know what the BSD device node is, unmount each partition on the drive without ejecting the drive fully otherwise it will disappear from Disk Utility. The partitions must be unmounted otherwise the following command will not work.
Open a new terminal window and type (without quotes) 'sudo VBoxManage internalcommands createrawvmname /Users/username/Desktop/USB.vmdk -rawdisk /dev/diskX', this will make a file called USB.vmdk on your desktop with instructions for VirtualBox to mount the desired disk inside the virtual machine. Make sure that you replace /username/ with your username and /diskX with the device node of the desired drive (e.g. /dev/disk1)
For some odd reason I have found that VirtualBox doesn't have permission to use the file you just created, so instead we must start VirtualBox using sudo in the Terminal by issuing the command 'sudo VirtualBox', this will open VirtualBox as root where the file can be used without any issues, Create a new VM using the desired settings but leave the hard drive empty for now. In the setting under 'System' make sure that 'Enable EFI', 'Enable I/O APIC' 'Enable VT-x/AMD-V' and 'Enable PAE/NX' are all checked and that the Virtual Machine is a 64 Bit Virtual Machine.
You will have noticed that after issuing the VBoxMange command earlier OS X re-mounted the drive, you will then need to re-open Disk Utility to unmount all the partitions of said drive before you can attach the USB.vmdk file to the VirtualBox, once the drives partitions have been unmounted you may attach the .vmdk file to the Vm by opening Settings - Storage then clicking the little 'Add Hard Drive' icon on the SATA controller. Once the file has been attached OS X may re-mount the drive once again so it would be handy to keep Disk utility open to unmount the drive again.
Once you have successfully attached the drive to the virtual machine you can attach a Windows ISO to the empty optical drive in the Storage tab and boot the Virtual Machine, Install Windows as usual completely erasing the drive and letting Windows do the rest. Once windows has done the initial install from the iso file you can then close Virtualbox and reboot your Mac to the external drive to continue the installation of Windows.