ChatGPT had more on Nolan. Oh yeah, THAT Nolan:
he work is usually cited as:
Nolan's System for Training Cavalry Horses (1862)
The historical chain is slightly confusing because:
the original ideas came from Louis Nolan, the famous cavalry theorist killed in the Charge of the Light Brigade,
but the American edition/adaptation was edited and expanded by Kenner Garrard during the American Civil War.
And yes — remarkably — it does include instructions for teaching horses to kneel and lie down.
The manual actually discusses:
kneeling,
lying down,
sitting up on the haunches,
even walking on the knees.
But there is an important caveat.
Nolan/Garrard themselves regarded much of this as:
specialized,
somewhat degrading,
closer to "performance" training than battlefield necessity.
The text explicitly says, in effect, "I publish this reluctantly." It describes the process as hard on both horse and trainer.
So your instincts are correct:
this was known in 19th-century cavalry circles,
it was sufficiently established to appear in a military horsemanship manual,
but it was not ordinary line-cavalry doctrine in the sense of "every trooper trains this weekly."
Rather, it sat on the edge between:
advanced horsemanship,
trick training,
practical field utility,
and exhibition riding.
What was militarily relevant was the broader principle Nolan strongly emphasized:
individual horse control,
responsiveness,
flexibility,
and using cavalry dismounted when appropriate.
That fits very well with Nolan's broader reputation as a reformer. He admired highly skilled irregular cavalry traditions — including Cossacks and other light cavalry systems — and pushed British cavalry away from rigid parade-ground habits.
So while the "horse lying hidden in ambush" image may sometimes be romanticized in art, the underlying skill itself was absolutely real and documented in period military literature.