Special Horses

It should be considered one, as it has its own series page.

My page does not say they are a special horse

Neither do the pages for Corgi, or Misaki, or Kirin, or Archimedes.
As far as I know, none of the special horses say that they are special horses on their page. However, all of the divines and other special horses are listed on the "Special Horses" page, including the Heritage Horses, so I think it's pretty safe to say that they are all considered special horses.

From their page on Special Horses:

The Heritage Horses
legacy
Heritage horses are special horses.
They represent the divine version of each breed in the Ephemeral breeds event

Clearly says they are special horses.

How do you get to the special horses page

Achievements>Special Horses.

If you have your own question, it's always best to make a new topic for it, as otherwise it can get lost in an already-answered question.

Or if you are on mobile the special horses page can be found by going into the trophy icon on the far right side of the navigation bar, then scrolling down to "Collections", then into "Special Horses". Pick a random divine family, and click on a divine from it that you don't own. Then hit "Find Out More". That'll take you to the special horses page

Thank you so much !!!