To run a VM as headless, make a Batch file containing:

cd "C:\Program Files\Oracle\Virtual Box"
VBoxManage startvm {uuid} --type headless

To run a headless VM at Windows boot, make a scheduled task that runs the batch file above. Make sure to disable the time limit on task.

To stop a headless VM, make a batch file containing:

cd "C:\Program Files\Oracle\Virtual Box"
VBoxManage controlvm {uuid} acpipowerbutton

This will shutdown the VM properly. If for some reason the VM does not respond to it you can us 'poweroff' instead. This simulates a hard shutdown.