This was universally known in the early parts of this century, but it appears to be universally unknown today. I have to constantly explain horses and apples to almost everyone who asks about "the Big Apple."
30 July 1927, Saturday Review of Literature, "Bowling Green" by Christopher Morley:
It seems queer that a man could be so ignorant. Do dogs like bones? Do horses like apples? Do Chinamen like rice? Do girls like fudge? That is how rabbits feel about plantain.
Horses love apples. But Chinamen like rice? Dogs like bones? Who understands that?
Here's a connection of "the big red apple" to a horse.
September 1898, The Century, pg. 677:
"SHE'S a darling!" ejaculated the bay mare, between munches of the big red apple.
"That's just what she is!" responded the carriage horse; and them, as part of the apple fell to the floor, he added fretfully: "I do wish, Lassie, that you girls wouldn't talk to a fellow when he's doing something! I've lost half my apple!"
Old Reveille, with the prudence of twenty-eight years of experience, carefully deposited the unmasitcated fraction of his apple beside an uneaten one in his manger before remarking reflectively: "She's lovely, but she's not the beauty her mother was at the same age."
"Fie!" exclaimed one of the cobs; "how can you be so ungallant, when she always gives you an extra apple or piece of sugar?"
There's also this:
17 October 1916, Milwaukee Journal, pg. 1, col. 6:
(An "APPLE DAY" cartoon shows a horse eating an apple--ed.)
"'SGOT OATS BEAT A MILE!"
November 1892, The Century, pg. 34:
"He was eatin' apples from the top of the tree. Horses like wild apples, and will lift themselves up to get at them."
Horses and apples: a study of index numbers
by Bassett Jones
New York: John Day Company (c. 1934)
This "applesauce" (a period slang term for "nonsense") popular joke involves horses and apples as well:
From the Evening Graphic (NY), "Your BROADWAY And Mine" by Walter Winchell, 21 April 1928, pg. 21:
The Wisecrack and the Gag
(From the October Bookman)
When big time vaudeville was downtown or where Mr. Keith's Union Square Theater used to be in New York, no bill was complete without that pair who swapped this one: "If you had eleven apples and twelves horses, how would you evenly divide the apples among the twelve horses?"
To which the "straight man," or the comedian's partner, would respond: "I don't know, Ignatz. How would you evenly divide eleven apples among twelve horses?"
"Why, you simply make applesauce!" was the answer and if the auditors didn't fall right out of their chairs at that joke, then the next generation employed the tag line of the old reliable to squelch a braggart or an opinion with which they didn't concur.
So great an army of entertainers employed the applesauce gag that it became the butt for derisive comment. It was in a class with "Who was that lady I seen you with last night?" or "Why does a chicken, etc.?" (...) "Applesauce!" said some one in the gathering and another wisecrack was born.
The flapper incorporated it into her routine of sassy answers, the collegiate passed it along to his towns fellows via letters and even the small-time and the big-time players "laughed off" a joke that failed to receive warm response from audiences by twitting themselves with "So we made applesauce!"
Horses definitely like apples but my horse would choose a carrot over an apple any day!