Just FYI, Hyper-V is not really a cloud solution. It's more like a direct competitor to VMWare. You setup a physical server as a VM server. Then create as many VM's on that box as desired. I use the Hyper-V Manager to connect and disconnect to/from my VM's running on this box as needed. They are left running and do pass, even those requiring an interactive desktop.
I agree Hyper-V is not a cheap solution as it requires both beefy hardware and a not-so-cheap Microsoft license. I have no idea the actual cost myself, it may cost the same as VMWare.
I've never used VirtualBox or VMWare myself, so I cannot say if it would or would not work. it might and, if you already have it, it's worth a try. The one thing I do know is that making the connection to the VM through Microsoft Remote Desktop connection, then disconnecting that session is not sufficient.