We had the "Songs of the West" album from Burl Ives when I was growing up, and I learned the version he sang more or less by heart. The following transcribes his version:

OREGON TRAIL
(De Rose/Hill - as performed by Burl Ives)

Wagon train a-windin' 'cross the prairie
Rollin' onward through the storm and gales
Toward the land of dreams trudge the old ox teams,
Down the Oregon Trail.

Through the night the Lord is in the saddle,
Ridin' herd beneath the moon so pale;
Watchin' o-er each stray 'til the break of day;
Down the Oregon Trail.

There'll be apples on each branch in Oregon;
There'll be valleys filled with golden grain;
There'll be cattle on each ranch in Oregon,
For there'll be plenty sun and rain

Hurry up, old pioneer, keep movin';
Your faithful little band must never fail;
'Cross the Great Divide side by side we'll ride,
Down the Oregon Trai-ai-ai-ail
Down the Oregon Trail.

[instrumental break]

There'll be apples on each branch in Oregon;
There'll be valleys filled with golden grain;
There'll be cattle on each ranch in Oregon,
For there'll be plenty sun and rain....

Hurry up, old pioneer, keep movin',
Your faithful little band must never fail;
'Cross the Great Divide side by side we'll ride,
Down the Oregon Trai-ai-ai-ail,
Down the Oregon Trail!

////

Listening to some of the other versions from YouTube, I get two more verses:

[Girls of the Golden West]

A smoke cloud in the sky, a savage drum replies,
There's danger on the road to Oregon
Through herds of buffalo, 'neath mountains topped with snow,
That's life on the Oregon Trail.

[Tex Morton]

An open range ahead, a blanket for a bed,
A friendly fire where lonely coyotes wail;
But wheels'll slowly creak; of home sweet home they speak;
That's life on the Oregon Trail.

For what it's worth, I don't know where I came across it, but I'm sure that I've heard the Girls' verse from yet another source, with the last line "We sing as we're traveling on" (which makes a good deal more sense in context, although it relies on the popular error of pronouncing Oregon as "Ory-gone").