“Why do cows wear bells?”/“Because their horns don’t work.”

A cow riddle Has been printed on many images:
 
Q: Why do cows wear bells?
A: Because their horns don’t work.
 
The joke has been cited in print since at least 1962.
 
     
9 December 1962, Indianapolis (IN) Star, “Riddle Box,” sec. 8, pg. 6, col. 6:
Why do cows wear bells?
Because their horns don’t work.
 
14 December 1962, Boston (MA) Globe, “Fun Time—The Riddle Box” by A. Leokum, pg. 35, col. 3:
Why do cows wear bells?
Because their horns don’t work.
       
Google Books
April 1963, Boys’ Life, “Think and Grin,” pg. 82, col. 1:
Joe: Why do cows wear bells around their necks?
Moe: I don’t know, why? Joe: Because their horns don’t work. — Garry Cronenwett, Galion, Ohio
   
Google Books
Puzzle Time
By Gerard Mosler
New York, NY: Scholastic
1979
Pg. 12:
Why do cows wear bells?
Because their horns don’t work.
   
Google Books
Best Ever Classroom Jokes:
Because some of us never grow up
By Mike Haskins
London, UK: Pavilion Books
2015
Pg. ?:
Why do cows have to wear bells?
Because their horns don’t work.
 
Reddit—No StupidQuestions
What’s the meaning of that joke: “Why do cows have horns? Because their bells don’t work”?
submitted March 5, 2016 by mmmrrr111
I’ve tried Googling but can’t find an explanation.
As a non-native speaker I can’t get that one.
Also, as I’ve seen someone saying that this version of the joke is wrong, this one is also good.
COMMENTS
evilmonkey2
I think you have the joke backwards. It’s “Why do cows have bells? Because their horns don’t work”
 
Cows typically (well, stereotypically like in cartoons…not sure if they do for real still, but they used to) wear bells around their necks. Horns have a double meaning: on the cow’s head or a car horn. Since the cow’s horns can’t make noise, that’s why they wear bells….cause the horns don’t work.
 
Get it? Hahahahahahahahaha. Oh wait…
 
Twitter
Reagents Specialty Chemicals and Solutions
@ReagentsChem
Why do cows have bells?
Because their horns don’t work!
#TellAnOldJokeDay
2:01 PM - 24 Jul 2018