You are right cold air is settling in the basement and not moving. It will leak down thru any opening and if you have an open return vent down there it will try to suck it down. You can do 2 things - install an air exchanger that sucks air down from the ceiling of the floor above and exhausts it at basement floor level, the reverse will also work especially if you have a warmer room upstairs that could benefit or you can open ALL the basement vents and run the fan continuously, on a lower speed when not cooling if possible.