POA's started out as Appaloosas/Shetland/Arabian mixes. The goal was to create a small, good minded, pony for children.
Nowadays they're breeding true (unlike "designer" dogs) so most POA's have POA parents. I'm pretty sure outcrossing with Appies, QH's, and possibly Arabians is allowed but I'm not sure 100%.
Personally, POAs are my second favorite breed. I just love their personalities. And those spots are adorable!
Here's a good link with information about the breed: Pony of the Americas - POA - Ponies & Breeds