Symphonic Dance: No. 4 Square Dance appears on the album “The Music and Art of J. Clifton Williams” by Rountree Wind Symphony.
This is what I could find out about Rountree Wind Symphony:
UW-Platteville’s Rountree Wind Symphony ensemble is a professional ensemble comprised of wind and percussion faculty members, selected students and alumni and regional professional musicians from southern Wisconsin and eastern Iowa. “The ensemble is a great opportunity for a select number of students to play alongside both professors and wind band professionals,” said Ellis.
And you can find out more about James Clifton Williams on Wikipedia.
I can’t find a full version of the song as performed by Rountree Wind Symphony online, but judging from this scratchy recording of the song being performed by the Heart of Texas Concert Band (Dr. Mark Rogers, conductor) in 2009, this doesn’t sound very square dancey to me, so it is getting filed under “not quite right“.