When you install an OS on a thumb drive, you're limited to the machine you did that on, right?
For licensing? I believe so but it depends on the OS. With Microsoft you aren't allowed per the license to install their OS'es on removable drives. There are hardware flags (coded into the firmware and hardware identifiers) that tell the OS if it's a "removable drive" or a non-removable drive. It's literally changing between a 1 & a 0 but you somewhat need to hack in to get there.
I Googled "make usb drive non removable" Somewhere in there it should get you pointed in the right direction if you really feel so inclined...
https://www.google.com/search?q=mak...l5.4655j0j7&sourceid=chrome&es_sm=93&ie=UTF-8
We run ESXi 5.1 (VMware) on 2.0GB (1.83GB usable) Kingston and Sandisk brand MicroSD cards. I run various other *nix flavors (CentOS and Mint) for some web servers, etc. on 16GB & 32GB USB & CF cards. On the 24/7/365 server machines it's good because the OS'es are fairly static, no disk defrags, no updates, etc. and it frees up an extra SATA power and data port. On the VMware ESXi machines we shove as many SSD's in there as we can for everything from VM/guest cache to actual boot drives, to deployment vehicles, etc. On the web servers it's great because we can take a tiny little pizza box, boot Linux or BSD off the USB, and have a full 3.5" HDD bay that's OS independent reserved for data only. (similar to putting your Windows OS on a small dedicated SSD)
When we switched over to Hyper-V from ESXi I was warned that not only are these types of media flagged as removable and therefore need to be changed (and you probably still are in violation of the license)... they also don't have wear leveling which means they will write to the same blocks over and over which will kill the drives faster and put you at risk for OS reliability. For reference I had ESXi (VMware) running from 4.0 through 5.1 over the course of about 3 years on the same 2GB Micro SD card... however I burned through a fairly high quality 16gb thumb drive trying to run Hyper-V in about 9 months.
If you really feel inclined to carry around your OS with you I'd do it via external sata (eSATA) and dump it on a laptop sized spinny drive or SSD. With the issues we had on Hyper-V I'd say that the Windows OS & kernel isn't really happy about USB 2.0/3.0 throughput speeds as your hosted OS drive.
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I was actually coming in here to post about something different. We use a bunch of cheap/retail 32, 60/64 and 120/128gb SSD's for VMs and virtualization. They are used to host VM operating systems, for VM cache, RAID array cache, and host cache. I've been upgrading the firmware on my SSD's the last day or so and I have to say the difference is night and day. Some of the drives the benchmarks are almost double. That said... I've bricked a few as well so whatever you do be careful or you'll have a dead drive on your hands. Don't attempt unless it's something you can go without for the RMA period.