Coulee is generally considered to be a Canadian French term, variously applied to a shallow ravine or small stream, sometimes to a dry streambed.
Merriam Webster's Collegiate Dictionary.

Versions have leading old Dan, Ball, Fan, or dam; take your pick. It is wrong to say that one is more correct than another.

Montana is a large and varied state, mountains and plains, good grass to semi-desert.

See preceeding posts re. hooleyann (hoolian) and hoolihan; usually the first is defined as rope work, the second as throwing a party (after the drive was over, etc.) or a rodeo type of roping, but both appear in versions and it is up to the singer.

Most of this has appeared in previous posts.