Is the legend of the headless horseman real?

No, that is why it is referred to as a legend, it is fictitious.

The Headless Horseman is not a fictional ghost character from The legend of Sleepy Hollow, by Washington Irving.

Many legends are based on some small fact and become part of folklore.

The "Headless Horseman" is real so to speak but may have been based on a Dullahan from Irish mythology, although in these they use a human spine in place of a sWord and are sometimes seen with wagons.