Not according to Sisson and Grossman, the absolute bible of equine anatomy. And horse breeders are among the most woo-woo people I have ever encountered. I sense some projection there. Both of these links are to layman's articles, and the second one is someone pontificating on a forum.
(As I said, a "persistent hymen" is occasionally encountered as a developmental anomaly in many species. It's not normal, but someone who has encountered it may get the impression that it is.)
Really? Because I don't only see the reference in horsebreeding stuff. I also see it in veterinary material from sources such as Merck (Merck Veterinary
Manual):
Perineal conformation should be evaluated. A manual vaginal examination should be performed to confirm the hymen is patent.
https://www.merckvetmanual.com/management-and-nutrition/management-of-reproduction-horses/breeding-soundness-examination-of-the-mare
Or this book, written by two veterinarians:
https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118904398.ch6
Not horses, but This paper talks about persistant hymen in alpaca and llamas. The discussion section describes the normal hymen:
The hymen is formed from the epithelial lining of the paramesonephric ducts and the urogenital sinus at the vestibulovaginal junction (3). Canalization of the hymen is usually complete at birth and leads to communication between the lumen of the caudal vagina and vestibule (3). Persistent or imperforate hymen has been described in camelids, but heredity has not been established (4).
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2572097/
The point is that a hymen is present in other mammals. The very fact that there is a condition called "persistent hymen" indicates it's existence during the development stages. From the artical above it appears that in the species discussed, it normally "canalizes" so it likely doesn't have the same effect as the human hymen unless there is a defect. But it does exist.
One last (non-authoritative) reference is this from straightdope:
Just one problem: Morris to the contrary notwithstanding, retention of the hymen is not unique to humans. It occurs in horses, whales, moles, mole-rats, hyenas, and perhaps other animals. (In the great fin whale, in fact, the hymen is not completely destroyed until childbirth.) Why? We haven’t got a clue. “Such adaptations [i.e., retention of the hymen] are explicable only if the male of the species finds it to his advantage to seek a virgin,” Bettyann Kevles observes in Female of the Species (1986). “But there is no evidence that mammal males seek inexperienced females, and no evidence that females with this peculiar anatomical feature remain monogamous. … In whales, one can explain the resealing of the vagina as a means of keeping water out of the reproductive organs.”
https://www.straightdope.com/columns/read/919/what-is-the-purpose-of-the-hymen/
The Morris he is referring to is the author of
The Naked Ape (1967) who describes it as exclusive to humans and attributes its function to discouraging young females from having sex too early/encouraging monogamy.

I don't think that's consistent with the evolutionary biology I learned in college, but I had more of an environmental focus.
But what is the point of this anyway? Is it to separate human sexual behavior from that of animals? To emphasize how much more traumatic intercourse is for human females than for other species? Or to imply that men are genetically coded to hurt women? Maybe it was just an aside, but asides usually have an implication.
As for animal behavior, animals have different social structures than we do. In ethology, I was taught that it's a mistake to try to ascribe motive to animal behavior, so I would say our understanding of those social structures is mostly empirical: who does the hunting, which males get to mate with what females, mating rituals, etc. The whys are often speculations that run the risk of assigning anthropomorphic traits, motives, and feelings.
So do animals rape? I don't know. Do male animals on occasion appear to be mating or trying to mate with females who are not interested or unwilling? I'll assume that such has been observed, but we don't know how animals of either sex view it. It may be completely insignificant or it may be traumatic. Or it may be just how life works for that species. So ascribing a concept as traumatic as rape to another species with which we cannot communicate is tricky. Adding hormonal signaling into the mix complicates it even further.
My point is if you wish to explain human behavior, looking to other (particularly non-related) species is tricky.