I am not sure how to answer this as a historian, but I do have some insight from growing up on a farm. I think this question has as much to do with economics as it does history or public opinion, but if a mod thinks that this approach is inappropriate for this sub, please feel to remove my comment.

In a nutshell, unless the public is willing to pay considerably more for horse meat than beef, it doesn't make any sense for a farmer to raise horses for meat. Horses are a lot more labor intensive, require more lot space, and don't put on weight as fast as cattle (though I am sure that last gap might be closed with selective breeding).

Horses require better pasture control than cows do. Horses are much more damaging to pastures than cattle. They tear it up almost as bad as hogs do. They prefer to keep eating the same low coverage, tenderer spots even though there is other good grass available. They are top grazers with their teeth. This, combined with their tendency to tear up the ground with their hooves means they will destroy areas of pasture if not closely managed and moved around often. Even when moved, the farmer has to be careful as if the new pasture is too good, the horses often overeat and can get sick and die as a result.

Cattle, on the other hand, will pull clumps off of the tall grasses with their tongue and graze more of the pasture. They eat more of the available foliage, thus the pasture gets better usage with cattle.

Horses are also mean. Thier bites are brutal and their kicks deadly. Sure, cows can bite and kick as well, but horses are much more aggressive. They also jump better than cattle, so you need higher fences. A single strand of electric fence is fine for cattle, but horses would jump right over it. The same logic on fences also applies to corrals and other more permanent fences. A standard 4.5 foot barbed wire fence is nothing to a horse.

Horses are harder to handle, meaning they require more labor and materials to manage. Their high metabolism and more active lifestyle (e.g., their love of running) means that they do not put weight on as fast as cattle. Thus they have a higher cost to raise, and less yield to show for it.

TL;DR: Unless people are willing to pay considerably more for horse meat, farmers do not have much incentive to raise them instead of cattle.

Of course, I focussed solely on raising horses strictly for meat, and not for raising them for one purpose (racing, farm work, etc.) and turning them into meat after that use is complete. That might make horse meat more affordable as it might just be a way to sell off a horse past their prime.

(Disclaimer: this is outside of my area of amateur study, and is merely part of a much greater narrative that hopefully someone more knowledgeable can flesh out)

There are at least a couple of horse meat shops in the 1940s in Newark, NJ that I'm aware of. One was called Whirlaway Meat Company, owned by Sam Stromeyer. The other was Man o'War Packing Co., which I can't find much information on. Whirlaway was the name of the 1941 Triple Crown winner, Man o'War was a legendary thoroughbred of the post-WWI time period.

I could only find a couple of articles related to Stromeyer's company (Whirlaway). Basically, he started it in 1941 and was active at least through 1946. (EDIT: Stromeyer claimed a 1941 founding date in an article linked below; however, this article from January 28 1943 in the Buffalo Courier-Express refers to the opening of said shop at that time.) I cannot find a founding date for Man o'War, but I have seen a storefront photo from sometime in WWII that advertised it as both Newark's first horsemeat shop and also one that could evade wartime meat rationing. (Note: I am still looking for an online version of this picture. Print source is on page 163 of The Home Front: U.S.A. by Ronald H. Bailey and the Editors of Time-Life Books. This is from Time-Life's series on WWII.)

The Office of Price Administration (OPA) remained active after WWII, and was blamed for postwar food shortages in a handful of articles from 1946. Whirlaway was still around in 1946, as Stromeyer is quoted in this Oct. 13 1947 Milwaukee Sentinel article about how two Boston-area hospitals were using horse meat for food due to shortages. The editorial refers to two 1946 stories, although the whole theme seems to involve how OPA price controls were terrible in this combination of eulogy and diatribe. (The OPA had been dissolved five months prior to the printing of the editorial.)

A Sept. 19 1946 article in the Mansfield News-Journal contained other quotes from StromeyerThis is also where his claimed 1941 founding date for Whirlaway came from:

Stromeyer, who was an automobile dealer back in 1941 when he decided that his present business looked more inviting, sells only for human consumption. "I' used to sell 5,000 pounds every other week for dog food," he explained, "but I quit. People were more particular about their dogs than about themselves. "They would order a roast and then yell, 'Now be sure that you cut off all the fat.' "

At a time that ground horse cost $0.21 per pound, compared to boneless cuts at $0.20 and bone-in at $0.16 per pound, respectively. He claimed to be selling 47,000 pounds of meat per week, and expected to hit 60,000 pounds a week once a looming trucking strike was called.

"It just shows how stupid OPA can be," Stromeyer said. "I went to Washington and explained to those people that a filet should sell for more than hamburger steak, but it didn't do any good."

As a postscript, someone named Louis Stromeyer from New Jersey was indicted in 1952 on charges of illegally labeling horsemeat as beef and then supplying it to a grocer in Danbury, CT. I do not know if Louis and Sam Stromeyer are related. Article is linked here.

This does not address OP's question with any real amount of information. All it shows is that for a period of time around WWII, at least two horse meat shops operated within a single city in the eastern United States and that shortages led to horse being used in hospitals. It does not address whether there was a taboo on horse meat at all, whether it was something that was considered too lowbrow to eat but emergency made it necessary, or whether it was more common but still something of a novelty.

Why is it so hard to find horse milk in the US?