You cannot use the "Install Windows From USB Flash Drive" program to reformat and copy ISO files to an external HDD. Windows simply does not recognize it as a flash drive (since it isn't one). However there is a fairly simple workaround. This question has been asked before on superuser. I do not credit myself for this explanation, but it was a lot simpler to just copy and paste than try to rewrite in my own words. I will link the full question page at the end, but notice the first response to the OP's question (the one copied and pasted below). It is by far the best and most thorough:
There is a fairly easy way to install Windows 7 from an external hard drive, and it takes less then 10 minutes to set up. You also don't need to switch to FAT32 to use this method.
First, format your disk as NTFS (quick format is fine, default sector size). Then, extract your Windows 7 disc/ISO to the hard drive. There is a utility included on the Windows 7 disc which allows you to mark the drive as bootable, located in the boot folder.
Once you're there, run BOOTSECT /NT60 X:, where X: is the letter of the external hard drive. Once that's done, you can just plug the drive into your computer, and you should be able to boot from it. Just FYI, the BOOTSECT tool updates the MBR for that drive's partition.
Alternatively, you could also just run the following command (from a command prompt or from the Run dialog, WinKey + R):
X:\boot\BOOTSECT /NT60 X:
Where, again, X: is the drive letter of your external hard drive. Once this is done, the hard drive has been marked as bootable, and if you try to boot your computer from it, the Windows 7 installation will be launched.
The reason they use FAT32 in that Technet article you posted is because those instructions were for a USB key. You can follow the DISKPART part of that guide to get your partitions prepared and setup, but do ensure that you format the drive using NTFS.
Here is the original post:
How can I install Windows 7 from an external hard drive?