Do Horses Exist in the MLP Universe?

[Valeska 184]

In our world horses and ponies are differentiated through height. An equine is considered a pony if it is less than 14.2 hands (4.73 ft) in height, while an equine is considered a horse if it is taller than 4.73 feet in height.

Does that mean, technically the ponies are really horses in MLP? Or are they just called ponies, while ignoring the definition of ponies in our world to make it more likeable to the intended audience? I'm just trying to wrap my head around this concept.

With technical definitions aside, are horses even a thing in the MLP Universe? The only reference to horses that I remember is the CMC's song "Hearts as Strong as Horses". Yet, the term "horse" hasn't been used anywhere else in the series as far as I can remember.

[Oleks 1,983]

Some people consider the Saddle Arabians - Haakim and Amira - to be "proper" horses - they have the height, the shapes and no cutie marks. But here it says that they are ponies anyway.

 

[Castle Bleck 19,172]

According to EQG, they're drastically different from actual horses:

 

[Yumekai 735]

It seems that they must be somewhere in the Equestrian universe because in the song "We've got hearts as strong as horses" they're comparing their determination or "hearts" to that of a horse so most likely there's other legends of horses passed down, or maybe just another loophole in the show.

[Valeska 184]

It would be fun if the writers played around with the idea of horses being a part of Equestria, because horses are one of the main types of equine. I could see horses in Equestria to be a wilder group of equine who rough it in herds, live off the native resources and live a very simple life.