I can't find the reference but I remember from somewhere that, as posted earlier, Woody made up this song for Arlo when he (Arlo) was a small child. The Woody Guthrie Songbook, Harold Leventhal and Marjorie Guthrie, Eds., 1976, has the song under the title "Riding in My Car" with the words and chords as posted earlier in this thread by Paul. I used to sing it to my kids when they were quite young and they loved it.

Reiver 2