Although the idiom to be cowed has nothing to do with Elsie the Cow, the use of corralled in a review of The Magical Chorus by Solomon Volkov in the Washington Post suggests a connection:
The culturati who would, could or should challenge it are cowed and corralled.
The transitive verb cow, meaning “‘To depress with fear’ (Johnson); to dispirit, overawe, intimidate,” may be from an Old Norse word meaning “to force or tyrannize over’.”
Sometimes cow is used as a finite verb, but more often it is used in the infinitive:
It [torture by al-Qaida] is used to intimidate the locals and to try to cow the populace in that area.
Syria and its allies may grow less subtle in their efforts to cow their opponents.
He would find it equally hard to cow the whole of the resurgent middle class.
The end of Thebes cowed Athens, leaving all of Greece temporarily at peace.
More frequently, the verb cow is used in the passive voice or as an adjective:
Outsiders need to speak up, since many locals seem increasingly cowed.
The men are cowed by the psychotic corporal, and a crooked sergeant is complicit.
Cowed and crushed, Jefferson accedes to his arranged defeat in Havana.
University students, once cowed by militias like the Mahdi Army, are feeling freer.
Sometimes cowed is followed by into:
A lot of women let themselves be cowed into giving up their dreams because of others’ expectations.
Time and again, rabbis assured that families were paid off, or cowed into silence.
Someone writing about Southeast Asia in Wikipedia follows the verb cow with an unnecessary down:
Though defeated by the Mughals he was never cowed down by their might.
Unwilling to be cowed down, Sikhs and Hindus counter-attacked and the resulting bloodshed left the province in great disorder.
A very strange use of cow occurs in this passage from a Politico article about a recent election rally:
The younger Trump marveled at the size of the crowd [and] held up the president as an outsider unwilling to cow to experts and institutions . . .
I suspect that the idiom being reached for here was not to cow, but to kow-tow.
NOTE: Both the kow and the tow in kow-tow rhyme with cow.
Presumably, modern Chinese no longer do it, but when China had an emperor, visitants to his presence were required to observe a ceremony involving the Great Kow-tow: three kneelings and nine prostrations before the throne. The OED defines it this way:
kow-tow (noun): The Chinese custom of touching the ground with the forehead in the act of prostrating oneself, as an expression of extreme respect, submission, or worship.
Figuratively, a kow-tow is “an act of obsequious respect.” As a verb, to kow-tow is “to behave in an obsequious manner.”
Here are some examples from the media:
Proffitt, in refusing to kow-tow to Murdoch, left HarperCollins.
He would raise no money, kow-tow to no special interests, and generally take no prisoners in an experiment in principled legislating.
Responsible, intelligent school administrators will put the students’ needs at the highest priority, and recognize that they don’t need to kow-tow to every crank opinion.
Expecting kow-tow to be a word unfamiliar to speakers under fifty, I was surprised to see on the Ngram Viewer that its usage tracks a steady rise from the 1880s to the present, showing a steep rise in the twenty-teens.
Bottomline: The difference between to cow and to kow-tow comes down to the difference between to intimidate and to grovel.