Can a VirtualBox Windows 7 virtual machine be installed on a USB hard disk? My MacBook Air has only a 64G hard drive which is so small that I don't want to install virtual machines on it. I'm planning to buy a 1TB portable USB hard disk to run virtual machines. Has anyone tried running a Windows 7 VirtualBox virtual machine on a USB3.0 hard drive with success?
Yes, it's possible.

First you need to create the virtual machine, after you completed the wizard don't start the VM but go to the menu Machine -> Show in Finder

Copy the 3 files (VM Name.vbox, VM Name.vbox-prev, VM Name.vdi) to your external hard disk.

After select the VM inside virtualbox and go to menu Machine -> Remove... and click the button Delete all files

After go to menu Machine -> Add.. and select the VM file you copied before.

Now the VM is inside virtualbox and runs from your external hard disk.