The colloquial American-English phrase to be all hat and no cattle and its variants mean:
– to have or cultivate a particular image or reputation which has no basis in reality;
– to engage in empty talk.
—Synonym: to be all mouth and (no) trousers—Cf. also gas and gaiters, blue sky and hot air and big girl’s blouse.

The phrase to be all hat and no cattle is now often thought of as referring to Texans—as exemplified by the following from ‘He’s a Texan, that’s all, big hat and no cattle’: Finley Recommends That Steelman Get Lost, by J. Russell White, Washington Star Staff Writer, published in The Washington Star (Washington, D.C.) of Thursday 7^th July 1977:

Former Texas Congressman Alan W. Steelman says there is still “a chance of a real sale” although Oakland A’s Owner Charles O. Finley is “mad as a hornet” over reports that Steelman is head of a group trying to purchase the A’s and move them to Washington.
[…]
Finley said he had nearly forgotten ever meeting Steelman until yesterday’s reports refreshed his memory.
“It looks as though Mr. Steelman is wishing to run again in politics,” Finley said. “He’s looking for publicity . . . This man pestered the hell out of me a while back, said he wanted to come to Chicago to meet me. That was three months ago, and I only saw him that one time. He’s a Texan, that’s all, big hat and no cattle.”

However, the texts containing the earliest occurrences of the phrase that I have found, in the form big hat—no cattle, indicate that it was originally attributed to Native Americans:

1-: By the U.S. Army officer, businessman, speech writer, government official and newspaper columnist Hugh Samuel Johnson (1882-1942):

1.1-: In The Oklahoma News (Oklahoma City, Oklahoma) of Wednesday 17^th February 1937:

Washington, Feb. 17.—“Seek a clarifying amendment, Mr. President,” prays Miss Dorothy Thompson.
In the mutual stately sayonaras of distinguished columnists—like encrusted priests saluting each other before the altar at mass—the only holy kiss ever offered this celebrant by Miss Thompson was “Frankenstein Monster” and “Big Wind.” The Osages say it better, “big hat no cattle.”

1.2-: In The Oklahoma News (Oklahoma City, Oklahoma) of Monday 15^th November 1937:

I started out by saying there is “talk” of a housing drive. Talk is all there is. There has been talk of it for exactly four years, eight months and 10 days. It is what the Indians, who also invented the word “bull,” “booshwa” and “boshee,” call “big hat—no cattle.”

1.3-: In The Evening News (Harrisburg, Pennsylvania) of Saturday 10^th May 1941:

With a terrible yell, a very young chief bounds to the center. His face and body are horribly streaked with yellow war-paint. The hawk-bells on his legs jangle fiercely as he spins and shrieks like a whirling Dervish. He waves an imitation bloody scalp (having never himself taken a real one for he is a phoney warrior) and calls for slaughter. He boasts of the prowess of his tribe and the weakness of their neighbors. He wants to blast Toh-Kee-Oo, the great war-village of the Ja-Pon-Knees, old and young alike, into a “shambles.” His name isn’t Senator Pepper. It is Chief Bo-Hee, meaning “Big Hat—No Cattle.”

2-:

2.1-: In the column Sol’s Sunshine and Shadow, published in The Ogden Standard-Examiner (Ogden, Utah) of Sunday 13^th February 1944:

A teacher called for sentences using the word “beans.”
“My father grows beans,” said the bright boy of the class.
“My mother cooks beans,” came from another pupil.
Then a third piped up: “We are all human beans.”
“After hours, win romance with a bright, sparkling smile.”
This is reminiscent of the Indian’s definition of a tenderfoot on a dude ranch: “Big hat—no cattle.”

2.2-: In Typical War Slogan: Patch the Patches, published in the Valley Evening Monitor (McAllen, Texas) of Monday 14^th February 1944:

“This reminds me of the Indian’s definition of a tenderfoot on a dud [sic] ranch: Big hat – no cattle.”

2.3-: In Patching Patches New War Slogan, published in The Brownsville Herald (Brownsville, Texas) of Monday 28^th February 1944:

“This reminds me of the Indian’s definition of a tenderfoot on a dude ranch: “Big hat—no cattle.”

3-:

3.1-: In an article published in several newspapers on Friday 27^th June 1952—for example in The Knoxville News-Sentinel (Knoxville, Tennessee):

‘Big Hat, No Cattle’

Members of the British Parliament who are demanding an equal voice with the United States in the conduct of the Korean war haven’t offered to share in the fighting on the same basis.
Moreover, while the British Socialists boast that they were responsible for Gen. Douglas MacArthur’s recall, they might add that their limited war doctrine also was responsible for the seemingly endless stalemate in which we find ourselves today.
Their free advice hasn’t suggested any honorable way out of that dilemma.
Somehow this situation reminds us of the loud-talking ranchman who applied to a western banker for a loan. The banker asked a neighboring Indian if he regarded the rancher as a good credit risk. The chief pondered the question a moment, and replied:
“Big hat, no cattle.”

3.2-: In The Grand Prairie Texan (Grand Prairie, Texas) of Tuesday 31^st March 1953:

A man whose business is concerned with finances, T&P Treasurer L. T. (Lee) McIntyre tells this one: A loud-talking ranchman applied to a Western bank for a loan. The banker asked a neighboring Indian if he regarded the rancher as a good credit risk. The redman pondered the question for a few moments, then replied: “Big hat, no cattle.”—TP Topics.

3.3-: In the column Making Conversation, by J. Emil Smith, published in the Illinois State Journal (Springfield, Illinois) of Wednesday 13^th October 1954:

This is the way I heard it:
A loud-talking ranchman applied to a western banker for a loan.
The banker asked a neighboring Indian if he regarded the rancher as a good credit risk.
The Indian pondered the question a moment, then grunted: “Big hat, no cattle.”