Here's a couple tips for a perhaps not so unique situation when using Hyper-V hosted in Windows 8 Pro with an ESATA spindle involved.
1) Moving a snapshot file to a different drive for performance reasons.
Hyper-V does not support keeping shapshot difference disks in folders separate from the base disk. If you're like me, and store the main VHD on an E-SATA disk, performance isn't bad, but could be much better if you could move the AVHDx file to a different physical drive, preferably a full speed drive. This issue is minimized with solid state drives, but if you don't have one, the best bet is to create your snapshot, remove the disk from your guest VM, move the AVHD file to an accessible location, and then re-attach it. (Don't take my word for it: back stuff up first!) Once you re-attach, it should run your read/write activities in the avhd, and pull data from the vhd file as needed.
[Edit: The trick to this part is figuring out where the config files are so you can modify them. They live at C:\ProgramData\Microsoft\Windows\Hyper-V\Virtual Machines\, but the files themselves are XML files with GUID names.
I typically find the correct one by simply looking at the modified date... it's probably the one you most recently used.
Before you can edit these files, you must shutdown the Hyper-V Virtual Machine Management service, and before you start it back up, you'll have to make sure that the account this service runs with has read/write access to the .avhd, wherever you put it.]
2) If your E-SATA drive is hardware encrypted, shut off power management.
One issue I was running into that was hosing the host and beating on the guest OS... My ESATA disk has a keypad that you have to tap out a PIN on in order for the disk to function. Power management was shutting down that drive at about 20 minutes by default, causing the disk to reset and disconnect, even with a VM running off of it... this is the computer equivalent of crossing the streams... suffice it to say it's Bad™. So using advanced power management, I was able to tell the system to stop spinning down the drives while the power cord was plugged in. (If I'm on battery, I typically won't be running my VMs on it.)