Children's series of horse books?

I'm trying to remember a series of books I liked as a kid. I think it was a series for young-to-middle-grade readers, one of those ones with a bunch of thin paperbacks, but that might just be me. It was about people at a stable, and I only really remember one book/part of the book. They went to some sort of horse fair [I think it was the heroine and her mother, who may have had a hand in running the stable?] and the heroine ran across a neglected mare who she later found out [I think possibly by listening to a conversation while hiding behind a van at night - random oddly specific memory that may or may not be true] that the mare was going to be sold to be made into...I think dog food, although my first instinct was glue. >.< Anyway, horrific crap for a horse-mad girl. So she convinces her mom [I think she was at the fair to find a horse to buy] to buy that horse for her. I also remember when they cleaned up the horse [I think a friend of the heroine was involved, as well as the mom?] she cleaned up pretty well, and when they were brainstorming names the mom came out with "Well my mom bought this old tapestry that was really dirty but when she cleaned it up it was really nice" and so they named the poor horse Tapestry. That's all I can remember, hoping someone can figure this out because it's bothering me. O.o