There are a few ways to cross the line if you ask me.
The first is if you are doing the same thing as everyone else. For example, breeding extremely dish-faced Arabians. There are people out there doing that. As far a I know, there are NOT people out there trying to restore the Kaimanawa.
The second is whether or not it truly is 'improving', or just making it look pretty. A pretty horse isn't a good horse. Breeding out conformational flaws, however, is definitely 'improving'.
The third links into number two. If the 'improvements' introduce more problems. I'm going to pick on Arabians again for this one because it's the main one I know about - When the dish in the face is too extreme, it can cause respiratory problems. Same with many breeds of dog, like the bulldog, pug, and cavalier.
But it sounds to me like what you want is to restore a breed, rather than improve it.
Just a little something you may find interesting. The Tarpan horse allegedly became extinct in 1909, but in the 1930's attempts were made to 'recreate it' by 'breeding back'
. It sounds to me to be similar to what you want to do, minus the fact that the Kaimanawa isn't extinct.
Personally, your aim wouldn't be classified as backyard breeding. Backyard breeding, to me at least, is breeding horses because they've got the bits, because you just want to, because you want money (Ha! Silly people), or some stupid reason like that. Breeding for a real purpose is completely different.