Can a horse with wings like Pegasus really fly if he was real?

Sure, if they have the musculature to flap and control the wings. They also need to be able to tuck their legs up to reduce drag.

No. Not without lots of magic. Gluing wings on a horse doesn’t give them the muscles, nervous system, brain, etc, involved in flying. And, horses weigh too much for wings the size generally shown, to let them fly. Even if they were somehow powerful enough, they wouldn’t really fly like a levitating horse so that humans could ride on them, since the force would lift from where they’re attached, and there’s nothing to hold the rest of the body horizontal if they’re not standing on the ground.

No. They are too heavy, the wings as they are usually depicted are too small, and the way the wings are attached to the horse shows there are no muscles attached to them. And the muscles they do have are way too small and weak. Remember that for a bird, in addition to the lightweight construction, breast muscles account for 20% to over a third of their body mass.
They could not even glide the way they are shown.

Nope. Look at the things that birds need to be able to fly. They need hollow bones to lighten the load. Eagles (a big bird) even have some extra bones that act as struts to give more structural strength. Birds typically have over developed muscles in the breast as well. These would be the muscles used to flap the wings. Additionally, as you add more muscles you need bigger wings. The horse has a whole lot of muscles that are used for usage when running on the ground. Wings would have to be significantly bigger than the body to be able to even consider something like this.

A horse would need a whole lot of redesign to make wings work

No. Agree with y’all above.

Such limited imagination.

If a winged version of Eohippus had evolved contemporaneously there would be a good chance it would have the musculature and bone structure of a flying horse,

It would need the wings of a 767 and the engines to boot!

It would have to be very muscled in its chest area to have the strength to get off the ground. I’ve been rewatching Game of Thrones and was wondering why the dragons had such a prominent chest when I realized that they would have structurally had to in order to properly use their wings to get off the ground.