Yes - but not a registered name or even an actual birth year. Do you have sire or dam lineage on her? Or even remotely? You can have all the factors you mentioned on any grade horse. Unless you have either who she couldve been out of, a hint at the registered name, and a birth year, I doubt you find her.
only other way to try and look is to see if APHA has anything listed to whoever you bought her from or bred her. Dont know if thats a way to search the actual registry or not.
also worth it to note - allbreedpedigree is a site people add their stuff to. Not every registered horse is on there. Only way would be to go through APHA itself.