My guess is that they were effectively horcruxes. Each copy split off a portion of Pinkie's soul to power it, placed in a magically constructed body. Think a Naruto shadow clone or Diary Tom Riddle.
I agree with the idea that as far as mind and memories went, they got only what Pinkie was concentrating on at the time, having fun with her friends. They were a reflection of Pinkie at that moment in time, not the full pony.
The original Pinkie changed after the mass of clones were created becoming listless and depressed, drained of willpower possibly a side effect of having so much of her soul removed. With Voldemort, it's fairly certain that having his soul split so many ways drove him insane.
This would also mean that far from destroying new lifeforms by returning the clones to the mirror pool, Twilight saved Pinkie's sanity by releasing the soul fragments to return to her. It also means that if the real Pinkie had been hit by the spell it would have no effect.
Though there is the possible Pinkie from Saddle Row Review. In the Xanth books it suggested that a partial soul would regrow over time. Maybe they missed one and that's what happened. If that clone was returned, it might be effectively killed, depending on whether it's memeories would be returned to the original Pinkie, as in Naruto.