Simply trying to determine if a horse of 30,000 years ago, considering evolution, could look EXACTLY like a horse today......
Probably. Why wouldn't they look the same? If the animal is suited to its environment, it will persevere. If it produces some mutation which branches off and is also well-suited to its environment, the mutant line will, perhaps, develop into a different (but clearly related) species. And the parent stock will also continue to exist, unless some calamity wipes it out. This is how evolution works. I'm really not following your question at all. Are you operating on some notion that every species MUST morph into something different every 247.5 years?