Now W10 Enterprise doesn't exist, it's still a technical preview.
Maybe with the final release you can do that.
You can try making a Windows to Go usb and then update it to w10.
What about an external hard drive?
As you asked the original question, riddle me this....
What is your end goal here ? Are you just going to use it for to run one computer, or are you looking for a portable OS to take with you ?
External HD drive, or USB drive, they will be treated the same way on a PC.
If your looking for portable, the best way would be like I said above with a VM on a USB 3.0 drive, as running the OS off the USB drive (booting the computer with the USB drive and OS installed on it) is very problematic at best.
If you want to try it, you should be able to use any of the 3rd party methods to run Windows 8 off USB drive, they should still work with Windows 10 (as I understand it, the sub system under Windows 10 is the same as 8/8.1).
Listen to my warning, I have tried to get Windows 7 and 8 running off USB (bootable USB drive that loads the OS), it's fine if your only using one computer but, after you start going to other computers, expect crashes and blue-screens. Not fun to troubleshoot...
When it comes down it windows is based on drivers, you need drivers for the hard drive, chipset, video card, and all other hardware, when you change hardware(take the drive in put in a different machine, drivers need to be installed, if it's funky hardware (not standard chipsets or video cards), it will give you a nightmare.
If you really want to "try it" search Google/Bing about running Windows 8 off a USB drive, follow the directions but, when it asks for the ISO, give it the Windows 10 ISO instead of Windows 8....
Post back on how you did, I am wondering how well Windows 10 works on a USB drive, I don't expect it to be any better than 7 or 8 tho...
I did a post on the forums here, go via my profile and you'll find something similar to How to make a WTG USB with 8GB USB
Edit - here is the forum link - http://forums.windowscentral.com/windows-8/318264-how-make-wtg-drive-8gb-usb.html
Great tutorial! Just need to find the USB... ��