White is not a recognized color by AMHA, sorry. Having filled out MANY an AMHA app for registration, I can assure you that the color "White" is not listed as a color choice.
Here is a list of the accepted color choices for AMHA Miniature horses... AMERICAN MINIATURE HORSE ASSOCIATION
I also want to point out that AMHA does not advise the riding of Miniature horses. If you read what you posted carefully, it clearly states that while they can be ridden by small children, caution is advised. If you read between the lines when they say "extremely adept at driving" they are saying that's what they are best suited for. A harness hardly weighs 25 lbs, either.
Honestly, the mare looks too big to have a set of AMHA papers.