I'm wondering when the last verse ("Dan's feet are sore ... ") was added. Presumably that verse is also by Bob Nolan, but I DK if it was part of the original song and just left off of the original Sons Of Pioneers recording.
The song was written by Nolan 5 years before the 1941 SOP recording, and it was recorded by Dude Martin that year (1936).
Also, Wikipedia and other sites currently describe Dan as a "mule." I've always assumed he was a horse - probably because so many horses were named "Dan" -- but do we really know what sort of animal Nolan conceived him to be?
Cptsnapper, Apparently Joni Mitchell (and maybe others who covered this song) rewrote some of the lyrics. I wonder if those alternative lyrics you remember were the work of Joni or another artist who modified Nolan's original ones.
FWIW, here is a partial list of recordings of "Cool Water:
Dude Martin - 1936 The Sons Of The Pioneers - 1941 Bob Nolan & The Sons of the Pioneers (feat. in the film "Along The Navajo Trail") - 1945 Jimmy Wakely & The Riders Of The Purple Sage (featured in the film "Saddle Serenade") - 1945 Bob Nolan & The Sons of the Pioneers (featured in the film "Ding Dong Williams") - 1946 Wesley Tuttle - 1947 Vaughan Monroe & The Sons Of The Pioneers - 1948 Nellie Lutcher - 1948 Jimmy Wakely (feat. in the film "Brand Of Fear") - 1949 Gene Autry - 1950 Billy May & His Orch. (vocal: Bob Morse) - 1953 Polly Bergen - 1958 Kate Smith - 1958 George Melachrino & His Orch. (Instr.) - 1958 Johnnie Ray - 1959 Marty Robbins - 1959 Jack Scott - 1960 The Browns - 1960 Frankie Laine - 1961 Eddy Arnold - 1961 Ramblin' Jack Elliott - 1962 Lorne Greene - 1962 Tex Ritter with Stan Kenton & His Orch. - 1962 Odetta - 1963 Slim Whitman - 1963 Patti LaBelle & The Bluebelles - 1963 Hank Snow - 1965 Tom Jones - 1967 Moe Bandy - 1982 Riders In The Sky - 1989 Michael Martin Murphy - 1995
Also recorded by: Roy Rogers Johnny Bond Walter Brennan Bill Black's Combo Bing Crosby & The Andrews Sisters Eddie Dean Fleetwood Mac Tennessee Ernie Ford Frank Ifield Burl Ives Sleepy LaBeef Norman Luboff Choir Jack MarshallR Rex Allen Mills Brothers Rooftop Singers Cliffie Stone Hank Williams Kate Smith Mason Williams Boston Pops Orch.
I think Tex Ritter's recording is the one that stands out in my mind (in addition to the Sons Of The Pioneers).