There are wild populations descended from the same ancestors as horses and dogs, those are not the same thing as wild horses and dogs. They have fundamental biological and behavioral differences.

Yes, domesticated horses and dogs can interbreed with their wild counterparts, but at that point you’re getting into the “What is a species?” question. Polar bears and grizzly bears can interbreed just fine if they’re in the same place, same for chimps and bonobos.

And for horses there aren’t even really still wild horses. There’s Przewalski's horse, but they separated from the ancestors of domestic horses long before domestication. They have a different number of chromosomes. Whatever wild horse populations we originally took the first horses from are long extinct.