This expression sounds American, specifically southern states American, and that’s exactly what it is.
‘All hat and no cattle’ is a later variant of the original saying – ‘big hat, no cattle’.
The allusion is clearly to the ten gallon hat – the oversize form of Stetson cowboy hat. These hats came into use in 1925, although even the largest held nothing like ten gallons of water. A city slicker wanting to pass themselves off as a rough, tough cowboy might wear the hat, but lay themselves open to the taunt ‘big hat, no cattle’.
The earliest printed example of the expression that I know of is from The Oklahoma News, February 1937:
“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.”
Many people associate the phrase with Texas, which is understandable for a phrase that connects cattle and bigness, both closely linked with that state. The early text above though cites the Osage Native American tribe, who originated in Kentucky.
The present variant ‘all hat and no cattle’ came into being much later – not until the latter half of the 20th century in fact. An early example of it, making the Texan connection, is found in Tennessee newspaper The Kingsport Times, July 1977:
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.