We sang this song around 1957-58 at Alexandria Elementary School, in Alexandria, Alabama. I remember a little paragraph with the song that said the words were written by a class of students somewhere. The picture that was on the page with the music was a group of wagons in a wagon train, of course.
Oddly enough, I remember the second verse better than the first. The second verse goes like this:

We will camp tonight, at a pleasant site,
And we'll sing to the banjo's strum.
To the fiddle's squeal, we will dance a reel,
And be happy all the day long.
Roll along Wagon Train, Roll along Wagon Train,
Roll along Wagon Train, Roll along across the plains.

First verse went something like this:
All across the plains roll our Wagon Trains,
On the way to the gold fields far,
dum, dum, dum, de dum......