It depends on several factors.
First is the version of windows you are using. With Win8 Enterprise, Microsoft introduced Windows To Go, which is exactly what you're wanting to do. But it's only for Windows 8 and it's only with the Enterprise edition. It doesn't work with 7, and older versions of Windows aren't even supported in the newest bootcamp.
Second is what kind of drive you want to install it on: USB, Firewire, or eSATA. The problem with USB & Firewire is that the drivers are loaded much later on in the boot sequence, so they can't be used for booting. I'm sure that the SATA drivers are loaded immediately, but I don't know if it's the same driver for eSATA and SATA.
Third, even if you manage to hack windows and mess with the driver loading (there used to be a way to do this with XP), you still need some sort of boot manager on the main internal drive to conduct a handoff to the external drive.
In summary, it's not technically impossible, but it's not very practical.
However, if your primary concern is storage on your main drive (and you had enough RAM), you could always load up Windows in a VM and keep the virtual hard disk on an external drive. No problems whatsoever with that (but depending on the drive connection, it might be slow).
