The murder motive turns out to be someone selling breedings from a lost stallion and the stallion's owner finding out by seeing the new foals listed on the online registry. However, equine registries generally require the stallion owner submit paperwork verifying a breeding is legit before they will register the resulting foal--it's how stallion owners are protected against stolen breedings and unpaid stud fees.
When they are looking at the records for each of the kids suspected of murder the top of the reports read "juvinile" instead of "juvenile".
When viewing the "USESA Registration and Licensing" for the horse, Kings Gambit, it says "Satus" instead of "Status".
While the movement King's Gambit performed when Folsom went to pick up his hoof, piaffe, is an upper level dressage movement it is not trained by touching the horse's foot.