Yes!

No question about it.

You can find a lot of old vet books at Internet Archive to see what they practiced then. You can find equally old medical (human practice) books.

At any period, vet practice does not lag much behind human medicine, if at all. We're talking about saving valuable property here, especially in race horses. If they are giving horses draughts of ammonia, odds are you will find the same thing being administered to humans (one of the treatments for the Spanish flu listed in, I believe, Henley's Formulas). I recently got a 1937 home medical encyclopedia, and found that mercury and lead doses were still in use as antibiotics, alongside sulfa drugs.

My husband was doing some research on veterinarians recently, and he found that the demands of vet study often make going to med school instead look easier by comparison. Your modern vet can treat any disease that shows up in both humans and a domestic animal species, like diabetes or cancer, and can treat trauma just as well, whether the patient weighs half a ton or half a pound.

In fact, in the 1860s, medical "science" is getting a bit stupid. You know how the role of citrus fruits in combating scurvy was discovered in the later 1700s? Thanks to the shortening (in days) of ocean voyages, and improvements in land dwellers' diets, scurvy was becoming kind of rare in the 1860s. So a certain French surgeon managed to promulgate the idea that scurvy was just a form of ptomaine poisoning brought on by improperly preserved foods. This lack of ascorbic acid in their foods helped kill a certain number of Antarctic explorers, like Scott, in 1912. So I certainly wouldn't want an 1860 MD if I could have a 2015 veterinarian treat me.