Depending on the severity of their problems they could also sell them or give them to someone, particularly if it's a long term issue.
If there's nothing wrong with the horse I'd try selling it first. Give it a try for a couple of weeks. If nothing turns up then I'd turn them over to a rescue. My rationalizing is that rescue organizations need to spend the most time and money on the horses they rescue from such places as abusive homes. If they can avoid putting extra strain on the rescues that would be best.
I'd take the horse if I could. :)