I have heard of people dumping horses (not necissarily in OR. I don't remember wear). And I'm pretty sure that it's frowned upon most places. Usually, from what I have read, they round up the horse and it either gets sold to auction, impounded (well..not really, but something like it), or sent to a rescue if the owner can not be found.
Similar to what County said, even if people thought these domesticated horses could survive running around on someones fields, they would stop it because those fields generally belong to someone who isn't going to be happy with a random horses taking up shop there.
I am all for animal advocacy groups, I just don't think violent protest is the way to get results. Buts that my personal opinion to most things.