Seems to have been calculated pretty consistently at about 3'6"/107cm:

Every time I see those real pony vs MLP pics I gotta roll my eyes a little because nine times out of ten the real world equine they use for measurement is either a fullbown horse or a very large breed of pony. A Shetland averages at three and a half feet, maximum. A Welsh pony stands anywhere from three to five feet, right in the range of somepony like Cheese Sandwich.

Judging by the height ratio above--which I take with a grain of salt, because cartoon stylization is a thing--the average adult Equestrian pony stands at the same height as a smaller breed of pony in the real world. Little Ponies are indeed as tall as actual little ponies.

Also, the only thing that separates a horse from a pony in the first place is being shorter than 58 inches anyway, so they're all ponies by default.

Another issue to consider with those comparisons is that most people figuring out their sizes measure the height to the top of their heads, but real equines are measured to the top of their shoulders. The pony in the third picture does seem to be on the tall side, but just comparing the raw numbers can be a bit misleading.