I tried with no joy. Period. Windows does not inherently install on an External HD on Mac. Using a tool such as AIK or a VM is no different and as much trouble as Boot Camp. Windows is a stable running environment with Boot Camp. Here are my personal tests and results using my Mac Mini as the lab rat.
Tools: Mac Mini (late 2012) 500 GB Internal SATA an External LaCie Thunderbolt 1 TB HD connected via Thunderbolt port and USB SuperDrive. Windows 10 Pro DVD created with MS Media Creation Tool. OS X USB Bootable Installer (El Capitan)
First test: Erased both HDD's GUID Partition Map, Mac OS Extended (Journaled) and performed PRAM and SMC. Note: Windows 10 will not install on MBR on a Mac.
Booted up Windows 10 Setup. Would NOT create partition on Thunderbolt - End of Story. So I was able to install Windows 10 Pro on Internal HD no OS X involved. Great, uh, right! Windows ran fine as Stand Alone OS for a few days. Ran in to booting issues, graphic artifacts and numerous little things of that nature. Moreover, there was no Firmware control. Windows cannot set or update the Mac Firmware or (BIOS) - it's not BIOS. So there was no command+R function without going right into Internet Recovery.
Second Test: Windows 10 still installed on internal HD, I installed OS X 10.11.1 on the Thunderbolt HD. All is well and good except, I had to unplug the Thunderbolt to boot into Windows. This became a mess. No stability.
Third and Final Test: (Current Config) Give the Mac what it wants! That simple. I left OS X installed on the Thunderbolt HDD named "Macintosh HD". Erased the Internal SATA and named it highly "Macintosh HD II". I used Boot Camp Assistant and moved the size bar until the Min. Setting of 13 GB. Installed Windows 10 Pro and I haven't looked back. The 13 GB "Macintosh HD II" sits quietly and holds bootcamp data from OS X/Windows. I don't miss the 13 GB partition and I Do Not Use It.
To sum it up. OS X will install on an External HD Thunderbolt or USB. Windows, even it's own Setup will Not partition or format an external device for Install. Windows Cannot be the stand-alone OS on a Mac as well.
These are my personal tests and findings using the tools and configurations explained above. Time consuming - Yes. Frustrating - Yes, (self inflicted). Worth the effort - Yes. Learnt a lot. Gives more of a definitive answer in this extremely long post of everyone with experience saying NO. You can't install Windows on an External HD with just OS X and Windows and Mac alone. Period. Hope this helps someone who has the burning desire to ask again. 😐
Cheers!!