Yes, it's possible and in an easier way than you could ever imagine. Since basically what we will do is install a copy of our OS in a flash partition so that when we go to another computer we only have to change the bios and start the OS from our portable flash memory.
Here I leave you the link of a detailed guide that I have gotten:
Yes it is possible to possible to install windows OS to a USB stick. In the last week I have tried this in my computer. I tried both windows and ubuntu by using a USB. The steps to make your USB for using Window are given below.
You can also install Ubuntu on a USB using this you can use two software at the same time. whenever you think of using just connect USB and use. Ubuntu is an open source system software. which is easy to use and most customizable system software. Steps to make your USB stick ready are given below.