According to Wikipedia:
The “sportsman’s deerstalker” is made with a brim around the cap, narrow at the sides, but which may be elongated in front or back, omitting the separate double bills. The earflaps are also eliminated. Some types of this cap sport a hatband fashioned from the same material around the crown. The “flapless” version can be easily folded for convenient carrying.
If you wanna see him in the hat..the Lady in Green is on TCM at this very moment.
The description of the hat is a “classic Trilby”
I’d call it a neckbeard hat, but I assume that’s not what they’re really called.
I don’t think they had Tinder back then 
Back when every Westernized man wore a hat every day, good bet the terminology was well-standardized and well-known to most people.
After 75-90 years of cultural inattention to hats, language drift, and the WWW’s billion non-expert monkeys each with a global megaphone? Not so much.
To an extent, you’re right. Most of the long coats that people call “trench coats” aren’t actually trench coats. Every man’s jacket is now described as a “blazer”, no matter what it actually looks like. Because most people nowadays don’t understand the specific features that differentiate these things from other things. Or care.
Hats seem to be different, though. From reading period literature, while yes, there were specific identifiable named styles of hats, there were also styles that were just called “a hat” or possible “a soft hat” because there wasn’t a name for the style beyond a description like “those sort of hats people wear when they’re casually dressed and wanting to look sporty”.
The wide brimmed wool hats that were commonly worn by cowboys (cowboys on the range did not wear bowlers), etc, the precursors to the Stetson had- afaik only one name, and that is a small and bad joke- they were called “wideawake hats” (the wool felt had no nap, get it??)
What about sombreros or slouch hats?
And bowlers were quite popular in the West.
Yeah, Sombreros were also worn, along with straw hats. Bowlers were a town thing, the Wild Bunch dressed up in suits and bowlers for a famous staged photo.
From the wiki article, see the picture of “An Arkansasfarmer wearing a wide-brim felt hat.”- that looks like the “wide-away hat”.
The title character of A. A. Milne’s poem “The Alchemist” wears one at night “so as not to go to sleep.”
You should read this. It might change your mind that bowlers weren’t worn in the West.
People confuse gunslingers and cowboys all the time. Very few of the iconic names of the old west belong to actual cowboys.
Farmer hats and western hats are so different.
Even in Arkansas.
I didnt say that, and yes, he is the author that started that ridiculous idea- and he has been castigated for poor research on several articles. What I said is that cowboys- on the range- did not wear bowlers. Townsfolk did.
Take a look at these period photos-
True, he does make a point- during the early or even “heyday” of the open range, Stetson wasnt making their famous “cowboy” hats, since Stetson wasnt founded until 1865- and the Boss of the Plains wasnt what we’d today consider a “cowboy hat”.
Teddy Roosevelt, writing during that period and in the West, even told a story about a cowboy who wore a bowler, and how they made fun on him, and worse.
True, but it was photos like the Wild Bunch that confused Beebe.
Lucius Beebe & Charles Clegg’s railroad books have come under scrutiny for their prose and reliance on anecdotal history both from contemporaries and historians since their deaths. A 1947 review of Mixed Train Daily praised the book for its broad scope and striking photography but criticized the text for its “pompous” tone, authorial biases and dubious claims.[21] Railway & Locomotive Historical Society (RLHS) founder Charles Fisher was an outspoken critic of Beebe’s writing and compiled several lists of factual errors he found in it.
Mad Magazine ran a whole article about that in the 50s:
If get the chance, you should check out the photographs of Francis Marion Steele and Robert McCubbin’s collection. They documented thousands of working men in the 1870s and 80s, often in candid, non-staged settings, wearing bowlers and other non-Stetson hats. The bowler was actually designed as a riding hat to stay on in high winds, which is why it was a functional tool for the range, not just a ‘town fashion’ for the Wild Bunch.
And the rounded shape kept it from falling off in mid-ride if a low-hanging tree branch brushed against your head.
thats a geniune Fedora …
pork-pies are very easily told apart: with a flat top and cylindrical (non conic) shape
I did for this artist, and i saw no cowboys with bowlers, there is this photo Cowboy Camp 1898 Na Group Of Cowboys Eating Beside The Irwin Brothers Chuckwagon Near Ashland Kansas Photographed By Francis Marion Steele 1898, which shows 7 cowboys, all wearing wide brimmed hats that look like wool- and no bowlers.
I then went to The Robert G. McCubbin Photography Collection | Old West Events which has some of his photos, and some of cowboys, all of whom are wearing wide-brimmed hats- and no bowlers.
The 1898 Steele photo shows the very end of the era, after Stetson’s marketing and Wild West shows had already standardized the ‘look.’ To see the diversity of the range, you have to look at the peak trail-driving years of the 1870s.
Also, look closer at the ‘wide-brimmed’ hats in McCubbin’s 1870s-80s photos. Most aren’t modern creased cowboy hats; they are round-crowned, stiff felt domes. The distinction between a ‘Boss of the Plains’ and a ‘Bowler’ at that time was often just an inch of brim. The bowler wasn’t a ‘town hat’—it was a riding hat designed specifically to stay on a rider’s head in the wind, which is why thousands of working hands used them before the ‘Stetson look’ became the official uniform.