The Old West (also sometimes called the Wild West) is the name of a culture and tradition that once existed some western parts of what is today the USA, Canada, and Mexico.
The old west is probably best known for the Cowboy. An animal Herder who tended to Cattle on Ranches on Horseback. These cowboys often lived a Semi-Nomadic lifestyle.
The Cowboy Hat and Cowboy Boots are also considered old west icons. And the commonness of carrying Guns (without being persecuted by governments or others) is also a motif of the old west culture.
My father told me that the old west still existed in some remote places in his life time. He told me that he saw it in some parts of Nevada. He mentioned that he went in a bar in Nevada, and you had people carrying Guns on them (just like you saw in the old west movies and TV shows), and you could even buy Firearms right at the bar!
My educated guess is that my father saw this while he was working for the USA Army. Which would put it at least as late as the 1940's. (It may have been later than that though.)
Old West Romanticism
There was a Romanticism that existed when I was a child and before that, during my father's life time, where telling stories about the old west became popular.
(The historical accuracy of some of these stories is questionable. But either way....)
As a child, I remember watching the TV show called the Lone Ranger, that was about the old west. I even had Toys of the Lone Ranger characters (and Horses).
It was even common for children to have Toy Guns (of the Revolver type guns used in the old west). (These toy guns were Semi-Automatic Double Action Cap Guns that, when loaded with "plastic caps" or "cap tape" would make a bang and give off a puff of smoke when fired.) I loved playing with these toys when I was a kid.
I even remember episodes of the original Star Trek TV Series having old west themes.
Remnants of the Old West Culture
Cowboy Boots and Cowboy Hats
I think the Cowboy Hat and Cowboy Boots can be seen as remnants of the Old West culture. In some places, like Texas and Alberta, wearing cowboy hats and cowboy boots are currently seen as "high class", and a worn on "special occations". (But, of course, many people wear them on non-special occations too... and just wear them as their normal wear.)
My Dad wore alot of Cowboy Hats. (Whether we were living in Texas or BC, Canada.) Also, I saw him wearing Cowboy Boots while we lived in Texas. (But he didn't wear them so much while we lived in BC, Canada.)
Both my bother and I wore Cowboy Boots, and even sometimes Cowboy Hats, from time to time, while we were kids. (Neither of us where them as adults.)
Some see Country Music as a remnant of the old west. But I don't know if country music even existed during these times and within the old west culture.
Regardless, both my mother and my father listened to country music, and I heard a good deal of it growing up.
Old West Politics and Wars
Some of the history of the old west is marred with the conquering of certain parts of western North America by the Government in the USA. From what I've read and been told, these series of wars, conquests was part of a political ideology called Manifest Destiny.
This Manifest Destiny and its Hegemony over the places where the old west existed eventually contributing of the whipping out the old west. And also had a devastating effect on the native and indigenous Amerindians.