As mentioned above, a good middle ground would be to simply delay closing the road until winter precipitation is actually accumulating. Or even to set up VMSes describing the road conditions and allow a driver to decide whether proceeding in their current vehicle is safe or not. After all, if you venture out on a snowy road and get stuck, or drive too fast for conditions and slide off the road, that's really your fault, not LaDOTD's.
I'll be in Shreveport next month en route to the Natchez meet, and if I end up encountering road closures when it's not even below freezing yet, I'm gonna be pretty mad. There's no good reason to close a road when it's 35°.
Consider this: Oklahoma City gets snow only about once a year as well, and you don't hear of the interstates here closing unless they are physically untraversable in an ordinary car. It may not be a good idea to go out on the Interstate, but that's not ODOT making that choice for you, it's you.