While having a Service is nice, you can do it with a scheduled task. Take system boot as the trigger, check the option to run the task without a logged-on user and set the action to
<VirtualBoxDirectory\VBoxManage.exe> startvm "vmname" --type headless. Make sure to remove the check from the incomprehensibly default-on option "kill the task if running for more than 3 days". Srsly, MS, what were you thinking, that no Windows computer would ever last that long without reboot?
There is a caveat: if a VM is started on boot that way, you will see it in the VirtualBox Manager as "powered off", so there's no button to show the display of the VM. There's only the "start" button and you will probably screw things up when you try to double-start it.
You can define a remote display port so that you can access the console of the VM thru RDC (mstsc.exe), without the VirtualBox Manager, but you still have to remember to not believe the "powered off" information. I don't know if that works better with a real service.