Although church authorities did attempt to root out the practice of eating horse in Northern Europe and the U.K. because of its perceived connection with paganism, there's no evidence that this was the decisive factor in turning popular sentiment against horse meat.
It seems far more likely that the aversion grew out of common sense home economics. Cows are just more efficient sources of food than horses.
Brian Palmer of Slate explains that in terms of caloric content, 3 ounces of cows give you more bang per pound:
A three-ounce serving of roast horse has 149 calories, 24 grams of protein, and five grams of fat. The same amount of beef tenderloin has 179 calories, 24 grams of protein, and nine grams of fat. Horse milk, which some Central Asians drink in fermented form, has one-third the fat of cow's milk.
To the contemporary eye, that may make it sound as if horse meat is healthier than beef. But that's only because we have ample sources of calories and fat available to us. For most of human history, that hasn't been true. Medieval residents of Northern Europe would have certainly appreciated the higher calorie, higher fat content of beef. Even without the scientific ways of discovering precise fat and caloric intakes, it would have been easy to notice that a serving of beef left you feeling more full than a serving of horse.
What's more, the different digestive systems of horses and cows mean that cows are more efficient eaters. A 2002 study published in the Journal of Applied Ecology found that horses eat 63 percent more than cattle. This isn't just a matter of bulk. Horses also eat more "digestible material" with actual nutritional content than cows, according to the study.
This is rooted in the differences between the digestive systems of the animals. Here's how Jessica Walling, a graduate student at Central Washington University, explains it at the Mustang Management blog:
[Cows and horses] diverged from common ancestors into two families known as Artiodactyla and Perissodactyla – ruminant and cecal digesters. Fermentation in the cecum and the rumen is similar. However, horses are only 70% as efficient as cows at digestion. This is because cattle regurgitate and chew partially digested food as "cud," repeatedly. Food is ground into smaller particle sizes. Another reason cattle are more efficient is because the food they intake is digested by microbes before it enters the true stomach.
Given a choice between raising cows and horses for food, it makes far more sense to raise cows. To put it differently, people who preferred beef to horse meat would have been healthier, heartier and used available resources more efficiently. They would, in short, have been more prosperous and successful. Over time, the beef eaters would triumph over the horse eaters.
While early Christian leadership may have nudged some in Europe away from eating horse meat, it's very likely the more efficient culinary taste would have won out even without a papal edict.