Humans aren't horses, but they're both mammals and so are likely to have fundamentally similar biochemistry.
Similar does not mean equal. Any pet owner can tell you that there are foods humans can eat that will harm your pets and vice versa. (e.g. Grapes, raisins, onions, & garlic can cause kidney failure in dogs & cats.) This is why we can't just stop testing with animal models.
There are a variety of drugs that are safe to use on horses but not on humans. One would be phenylbutazone, or "bute," a painkiller that will suppress human white blood cell production and, in conjunction with some other drugs, will destroy your liver. Bute is one of many horse NSAIDs not approved for use in humans.
(Similarly many human OTC painkillers in the same class will kill your pets. Tylenol is also bad for pets, causing anemia in cats and liver toxicity in dogs.)
I can't find anything about dewormers being poison, though. Apparently, most of the dewormers I saw were also used (in appropriate doses) in humans and dogs or simply have never been tested properly in humans. I looked up fenbendazole (not enough testing), ivermectin (used in humans), moxidectin (not used in humans but safe according to some tests I read), praziquantel (limited use in humans), and pyrantel pamoate (used in humans, but an uncertain risk to pregnant women). With the exception of the last, I'm not aware of any known risks from their presence in meat, but we just do not have enough knowledge on many to approve it for the general food supply.
(On the subject of dogs, it worth noting that a few of these drugs -- the avermectins -- can be toxic to herding dogs but not to most other dog breeds. It makes their use in heartworm medicine tricky.)