I’m pretty confident in saying that neither unicorns nor flying horses exist, but your question brings up some interesting questions like, how can we ever say that something doesn’t exist? And why do we have legends about things that apparently don’t exist?

The unicorn legend may have come from people seeing horned animals from the side, where one horn would hide the other one. This would make the animal look like it only had one horn. Can I say for certain that they don’t exist? I really can’t. You can have evidence that something does exist, but not proof that something does not exist. Maybe there are unicorns hidden somewhere and we just haven’t found them yet. We are still discovering species, even mammal species. It just isn’t very likely that something as big as a horse is somehow not being noticed and that no one has found any bones or fossils of them.

A flying horse like Pegasus is probably purely wishful thinking. I doubt anyone thought they saw one, they probably just wanted to. The legends of Pegasus and other flying horses come from a time when the fastest way to travel on land was a horse, and there was no way for humans to fly. I can tell you that flying horses don’t exist because, we’re talking about whether something is physically possible. Physics and anatomy tell us that a horse with wings would not have enough power-to-weight ratio and would not be aerodynamic.

It’s not physically impossible for a horse to have wings, I suppose, but big useless wings are extremely unlikely to evolve. Can horses with wings exist? Well it’s extremely unlikely, but not impossible. Can horses fly? Nope. Can you see the difference between whether something exists and whether it works?

It’s interesting to wonder why some people believe stories about mythical creatures. There are apparently people watching TV shows about searches for Bigfoot, a human-sized primate that is supposed to be roaming around areas of the US. Why do you think belief in these things is popular?

Personally, I find real animals so incredibly fascinating and surprising that I’d rather learn about them than believe in mythical things, but that doesn’t mean I wouldn’t enjoy a daydream about having a horse that could fly.

Not in the classical sense, no, unicorns do not exist neither Pegasus.

However, the original Greek description of a unicorn is that it is an animal with a single horn in the middle of its forehead, the legs of an elephant, and a ferocious temper. Add these together, and you've got a pretty good description of a rhinoceros. Are unicorns really just rhinos? Rhinos certainly do exist!