Slim Critchlow's version is similar to the Larkin one posted by Q, but there are significant differences. Slim gives no information about his source, but has an extensive note on technical terms which I have reproduced below.

WINDY BILL [Slim Critchlow's version]

Windy Bill was a Texas boy,
And he could rope, you bet,
He swore the steer he couldn't tie
He hadn't met up with yet.
But us boys we knew of an old black steer,
A regular old outlaw,
That ran down in the mal país
At the foot of Rocky Draw

This old black steer had stood his ground
With the cowboys from everywhere,
So the boys bet Billy two to one
He couldn't quite get there
So Billy brought out his old grey horse
His withers and back were raw,
Prepared to tackle the big, black steer
That ran down in the draw.

With his Brazos bit and his Sam Stack tree,
And his chaps and taps to boot,
And his old maguey tied hard and fast,
Bill swore he'd get that brute.
First, Billy sort of sauntered round
Blackie began to paw,
Then he twirled his tail up skyward,
And went a-driftin' down the draw.

The old grey horse flew after him
Like he'd been eating corn,
And Billy hung his old maguey
Right round old Blacky's horns.
The old grey horse he stopped right still,
The cinches broke like straw,
And the Sam Stack tree and the old maguey
Went a-driftin' down the draw.

Billy lit in a pile of rocks
And his face and hands were scratched,
He said he thought he could rope a snake
But he guessed he'd met his match
He paid his bets like a gentleman,
Without a bit of jaw,
And he 'llowed Old Blacky was the boss
Of anything down that draw.

There's a moral to my story, boys,
And this you all must see,
When you go to rope a snake
Don't tie it to your tree
But take your dally weltas, [dar la vueltas]
'Cordin' to California law,
And you'll never see your old rim fire
Go a-driftin' down the draw

Source:   Slim Critchlow 'Cowboy Songs: The Crooked Road to Holbrook' Arhoolie CD 479.

Slim's note to this song is as follows:

Although a comparatively short song, 'Windy' has the distinction of having more technical terms per line than any other song I can think of. It'll take more than a few words to tell you about this one! It's one side of the story of an argument that has been going on for a hundred years between the 'dally ropers' (an English corruption of the Spanish 'dar la vuelta' meaning to take a turn around the saddle horn) and the 'hard and fast' ropers from Texas, Arizona, Utah, Hawaii and other points – depending on how they were raised – who used a shorter rope tied to the saddle horn. The brush poppers had no time for a dally. They threw a small loop whenever they had room enough to fit it over the steer's horns.

Bill was evidently a fellow who used his saddle stock hard and rough judging from the fact that his horse's withers and back were raw, so maybe he deserved what he got. His saddle was what was known, and still is in some parts of the country, as a 'rim fire' or Spanish double, meaning that the front cinch hung directly beneath the saddle horn, the back cinch loose just to keep the saddle from tipping up when the roper made his catch.   Saddle rigging is graduated from the full double to the 7/8 double, to the ¾ or 5/8 either single or double and finally to the ½ rigging or 'center fire'. You can't hardly find any of those any more. Both 'rim fire' and 'center fire' terms stem from the time when metallic rifle cartridges came into use and rifles were chambered for either a rim fire or a center fire shell.

The old black steer had his home in the rocky, brushy country – the mal pais or bad country and steers like Old Blacky became as wild as any animal could be. Bill's saddle , or tree, was made, according to the song, by Sam Stack (or Stagg, as the case may be) who was evidently a well-known saddle maker in Texas. His rope was a Mexican grass rope made from maguey fibres, shorter and stouter than the rawhide riatas used by many of the dally ropers back when this song was 'composed'. His 'taps' or tapaderos were short leather shields to keep the brush out of his stirrups, his bit was evidently a spade or curb peculiar to the Brazos River country, and 'snake' was a term sometimes applied to a real ornery outlaw steer.

And that just about takes care of Windy Bill. He may have lost his saddle but he'd never lose a finger or two getting caught up in a dally. [Slim Critchlow from booklet insert to 'Crooked Road to Holbrook].

--Stewie.