Hot Add Storage was added to Hyper-V at version 2008 R2.
The Drive is now attached to the machine so all we need to do is login to the machine, bring the disk online, initialize it and create the volume.
You will now have access to this new drive in the virtual machine
If you want to see the same process using System Center Virtual Machine (SCVMM) Manager see my Video of the process at Hot Add Storage to Windows Server 2008 R2 Hyper-V Guest Using SCVMM