Hello,
It is, in fact, possible to install windows on an external hard drive. I have done it using an external HDD. I did it with windows 10 but I am pretty sure it works the same with Windows 8.1. The guide I used can be found here:
https://discussions.apple.com/thread/5431182?tstart=0. Look at the first reply with the 20 steps.
However, as chscag already said, windows are not meant to run on an external storage unit. Furthermore, even though you can install windows on a 32GB thumb drive, the storage left after the installation will be ~20GB, which in my opinion is not enough to do many things. Then, the connection between the drive and the mac should be fast (USB 3.0) or anything superior. Finally, as I said before, you are not supposed to run windows from the thumb drive, so expect a bunch of problems. In my case, the connection between the drive and the mac was not always stable, so sometimes the os just crashed, giving the 'INACCESSIBLE BOOT DEVICE' error message.
TL
R Yes, you can do it. No, I do not recommend it.