Installing mint to usb drive is the same as installing it to a hard drive...... No Unetbootin... not necessary
Insert your usb drive.
Boot your mint live cd.
Choose install mint.
When asked where to install... go to manual/something else.
Choose the usb drive....MB size should lead you to it.
Set grub to install to the usb drive to.
After installing reboot pc... make sure usb drive is the first boot device.
Now you have a fully working mint pc running from your usb drive...... not a live cd type environment.