Evidently there are two quite different "Cowboy Waltzes"; the file I pointed you to is the same tune that may be had at the Henry Moore collection,  here; the one you're after doesn't seem to be available anywhere in staff notation.  There is a Real Audio clip of it, though, recorded by Woody Guthrie and Cisco Houston, at  Buffalo Skinners (Smithsonian/Folkways.

It's less arranged than the example you mentioned, so you may find it easier to learn by ear -which you'll have to do, unless somebody finds what I couldn't!

Malcolm