I am almost certain it's a Woody Guthry song-- as is "the wheel of the bus go round and round" (that is definately a Woody Guthry song!)

some of Woody's songs entered the mainstream so quickly-- it was as if they were always there..

Like Tommy Makem's "Four green fields"-- original written as a commercial "background song" for Aer Lingus-- which many now swear is as old as the hills being sung about... and a "traditional song"

meanwhile other traditional songs-- Wabash Cannonball, ie, which is a traditional song, author unknown, have one "version" copyrighted, by one person-- who then try to demand royalties!

Arlo said one of the joys of his childhood, was going to school and having teachers "teach" him songs his daddy wrote!