Okay, the noun is: das Pferd.
You need to "decline" adjectives in german.
Ein does not tell us any information (and German needs it!).
So the information gets passed to the adjective (klein).
So: Ein kleines(because of the das) Pferd.
So the adjective 'klein' now shows us the missing 'das'.
This is extremely over-simplified, but there are a lot of helpful charts out there to look at for this.
Because Pferd is neuter, not masculine or feminine, so it takes 'ein' instead of einen or eine.
Someone else posted this link, and things began clicking for me. I'd love to give credit, but I forget which thread it is.
This occurred on another question. Without the adjective, this would be "Sie hat eines Pferd" for an article in the accusative case (right?). Why does that get thrown out the window here? Is it just the article that suddenly doesn't need to be declined? Is it everything except the final adjective?