Hyper-V does VSS snapshots of VM's, and if those OS's have the integration services installed, it will notify the internal OS to also prepare for a snapshot. That VM OS then tells any apps that have VSS providers to flush to disk (known as Quiescing). So the cool thing is the VSS notification trickles down from Hyper-V->VM->Apps in VM. The bad thing is it only helps for apps that are VSS aware. VSS has in been in Windows Server since 2003, and is widely supported on Microsoft products but not so much in 3rd party.
So it seems MySQL doesn't have native VSS support but there is a third party tool according to this.
If it was me, I'd set MySQL to do DB and Log backups to local disk (frequently, maybe even every 15min depending on your Recovery Point Objectives) and still do the Hyper-V snapshots to capture those files. In a recovery scenario if you have any data loss you can recover from those rather then only have the online (open files) MySQL DB's and Logs. Note that I'm not a MySQL expert 🙂
