Here's an interesting article from Arizona about just the kind of legal quagmire that "abandoned" horses create.
This case is a good illustration of how:
(1) It's often unclear exactly whom should be notified when horses are found, and even law enforcement may not be able to tell you the right answer
(2) Failure to notify the appropriate authorities can have negative financial consequences for the finder of a lost horse
(3) Even months and years after the horse goes missing, the lawful owner can reclaim the horse
(4) When reclaiming the horse, the lawful owner may be able to avoid reimbursing the well-meaning people who have paid to take care of his horse
(5) The fact that the horse was donated to a rescue and adopted out to a third party does not necessarily change (1) - (4) above.