I will preface this by saying I'm not an expert on archaeology, or on pre-Columbian history of American indigenous peoples. But I am a trained academic, and I know some things to watch out for when giving something a critical read. I will also preface this by saying I have not read the dissertation in question, either, so some of what I have to go off of may also misinterpret some of the findings.

But I did find at least one review from an Archaeology blogger that is highly critical of said dissertation. I admit when I read the piece in the OP, a few things raised my hackles and made me suspicious. While I don't want to engage in confirmation bias, the writer, Carl Feagans, points out many of the potential errors in Collin's study.

What she noticeably omits in this literature review are biological, paleontological, and genetic sources of information. If one has a hypothesis regarding the existence of a mammalian species, one expects these in the literature review. No doubt Collin would have us believe that Native American oral tradition is trustworthy because cultural tradition and linguistic style was guaranteed to ensure fidelity and preclude embellishment or omission of facts inconvenient to the narrative.

That is a big red flag. When one is making an extraordinary claim against what is generally accepted consensus, there ought to be extraordinary evidence for the claim in question, which would include biological data on various horse species and subspecies. If Collin did not at least include these in a lit review, that's already a bit of a problem. While historians do not have to be experts on every subject, historians of science, or those who study sub-fields like epidemiological or environmental history, often have to include major scientific publications in their lit review so that they have sufficient familiarity with the field and its lingua franca.

For instance, a basic search on an academic database for New World genetic diversity among horses revealed this article, which seems to support an Iberian origin theory for most horses in the Americas. I am certainly open to seeing data to the contrary, but I was not able to find it in my relatively short dive into the topic to reply to this post.

There are other places where Collin, or Lyla Johnston (the author of the Indian Country Today article) seems to engage in specious reasoning. Take the following:

“We have calmly known we've always had the horse, way before the settlers came. The Spanish never came through our area, so there's no way they could have introduced them to us," reads one quote from a Blackfoot (Nitsitapi) study participant in Collin’s doctoral study.

That's a strawman. No serious scholars are suggesting that every reintroduction of the horse into the New World was via direct transmission from the Spanish. Capture of feral horses and trade between Native peoples undoubtedly had far more to do with the propagation of the horse throughout the continent.

Another problem appears to be that Collin (or at least Johnston's presentation of Collin) seems to cherry-pick her data without providing sufficient context.

Collin also drew from interviews with American Indian study participants from seven different Nations. Every indigenous community that was interviewed reported having horses prior to European arrival, and each community had a traditional creation story explaining the sacred place of the horse within their societies.

“I didn't expect that,” says Collin. “If you lay out a map, these Nations are all over the place. These communities do not speak the same language, share the same culture or the same geographical areas. Yet, their oral histories were all completely aligned. They each shared when the horse was gifted to them by the Creator, that the acquisition was spiritual in nature, and that they did not receive the horse from the Europeans.”

Which Nations? From what period do these narratives date? What is your evidence for dating them as such? Collin rightly points out the linguistic diversity and complexity of indigenous languages, but that on its own is not proof of superior memory or accuracy of record.

Then we come to another eye-brow raising problem.

In a recent interview, Collin gave greater insight into the political and cultural nature of science. In April 2017, mastodon bones with designs carved by human hands were dated in San Diego showing human presence in the area as long as 130,000 years ago. This scientific dating is drastically different than the dates previously given by Western academia regarding how long Indigenous Peoples have existed in the Americas. Such dates only went as far back as 10,000 to 15,000 years at most, explained Collin. Again, many Western scientists expressed initial disbelief and even outrage with this new evidence. Collin finds a parallel between the reaction to these new Western findings and that of the fossil evidence showing horses were always in the Americas.

The fallacies abound here. One is a general error in thinking that Michael Shermer identified as "Heresy Does Not Equal Correctness." People making unorthodox claims often point to the persecution of Galileo, the resistance to germ theory, or opposition to Einstein as proof that their unorthodox idea must also be correct, but the establishment (academia, "Western" science, the elite, whoever) won't accept their findings because they are too steeped in orthodoxy. This is definitely a danger in any organization, academic or otherwise--the conventional wisdom can go unquestioned for far too long. But in all of the above cases, the "unorthodox" positions were eventually accepted because the evidence was eventually just too compelling or overwhelming to reject. It is the evidence, not the unorthodoxy of position we should examine. And in the case of this April 2017 study, Collin unfairly lumps in detractors as "Western scientists," as though the claims were not also made by "Western" authors. Here is an article from Nature that summarizes some of the claims and the potential shortfalls of said study.

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I read this thesis. It is provocative. I think it should not be considered a settled question. Some archaeological digs may have had horse bones mislabeled post-Columbus. But she did not provide compelling evidence to the continuity of horses to present day.

The evidence presented does not mean horses did not go extinct. There was a considerable extinction of large mammals at the end of the Ice Age in the Americas, as well as elsewhere in the world. Genetic analysis of mustangs do show a link to Spanish horses, but that may be simply from heavy crossbreeding.

There were prior contact with the Americas from Europe. Vinland, for instance, was settled around 800 and abandoned by 1000 AD after conflicts with what sources called "Skraelings" and are thought to possibly have been the Inuit.

We have no proof that the Vikings brought over or did not bring over horses. I think there is a chance they did.

However, at this point the answer would also be established by sampling horse diversity overall in the Americas vs elsewhere. If her thesis is true, native American breeds should have genotypes not found elsewhere (since it is where horses originated.) or show kinship with East Asian breeds in ways not found elsewhere (assuming a continual population until Beringia vanished, which is not automatically likely.)

We have recently found the Przewalski's horse (not related to domestic horses) are linked to horses captured or tamed by the Botai peoples. The genetic distance is estimated at 160,000 years ago. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8018961/

You would expect any remnants of the Native American horse to have genetic diversity that encompasses all the known horses (Przewalski's horse) and then some.

Verdict: unproven, certainly important not to assume the Spanish reintroduced the horse to America and there were not some feral herds prior to Columbus, and to search the archeaological record and test DNA of horse bones accordingly. that's how science works.

You take the hypothesis (all horses in America soon after Columbus were exclusively Spanish import or descended from such) and test that with contemporary digs and other evidence (oral narratives can matter, would be nice if they were recorded 100 years ago or more.)