I'm not sure if this answer is too much of an ecological one. Mods can decide if this veers too far off topic.
The short answer is "There are feral cattle in North America" ^1 . I didn't manage to dig up any official census on historical feral horse or cattle populations, but I think it's nearly undeniable to say that there were examples of each.
Given that there were at least some feral horses and feral cattle, what else do we know about the historical situation they were found in? While we don't have historical accounts of animal population sizes until much later in North American history, accounts attest to the early spread of horses without human, or at least European management ^2 . Overall domestic horse populations wouldn't peak until much later as humans continued to bring over horses and breed them for use as labor and transport ^3 . As mechanization took jobs from horses, horse populations fell, but cattle populations would continue to grow into the 20th century ^4 . So, given there were fairly comparable domesticated populations, at least as far as I can tell, why did horses spread across America (geographically at least, if not by population) while cattle did not?
As you might know, horses are actually native to North America, or at least, their pre-domesticated ancestors are. Early horse ancestors struggled to adapt to earth's cooler climate in the late Eocene, around 40 million years ago. As North America dried up, forest gave way to grasslands which favored long legged three toed and single toed mammals. We don't know which specific ancestor is the direct parent to Equus, but we do know that by about 4 million years ago horses could be found everywhere from Florida to Idaho. Clearly a successful species, horses would make their way into Asia via the Berring land bridge sometime before 2 million years ago. Horses would remain in North America along with several other cousins, until most North American mega fauna died out around 11,000 years ago at the end of the last ice age, including all forms of horse.
As the North American Horse died out, it became smaller and more suited for forests and hills ^5, and it's likely this is because horses were competing with a soon to be very successful animal, the North American Bison ^6 . Unlike horses, bovines never left America. For the next 10,000 years Bison would struggle with their own ecological adaptations ^7 but would not vacate their ecological niche the way horses did.
The horse would return with Spanish settlers in the early 1500s. There are reported populations of feral horses as early as 1550 ^8, but these horses were not identical to those which had died off in North America a few thousand years before. These had been domesticated to survive and thrive in the new Holocene grasslands that now covered vast areas of Asia, Africa, and now North America. Time had made their place in the North American ecosystem more hospitable, and they spread into their old home once again. There's certainly something a little romantic about this American animal returning to it's homeland, but I'd caution against any tale that they dominated North America. Wild populations existed and thrived, but without hard numbers, we can only guess as to their exact success.
While this is a compelling tale for horse populations in America, I'm not quite sure it's as satisfying as answering "Why didn't cows do the same thing?". I can offer up some thoughts, such as their ecological niche being filled by the incredibly successful plains bison as I mentioned above, or that human use of horses for transport favored their spread more than human use of cattle for livestock, but ultimately those are speculation. Good historical answers for things that happened largely outside of human observation hard to come by. At least comparing and contrasting the history of these two animals provokes interesting observations.
This is a question (someone knowledgeable on the topic please set me straight): is not the spread of feral cattle in the plains of Texas (especially in the post Civil War era) an example of something comparable to the spread of feral horses actually occurring?