I've never seen a horse there, but I've never seen anything explicitly stating you can't have a horse. The beach can get pretty crowded and there are frequently dogs off leash. I would keep that in mind. Your best bet is probably to call the Oregon Parks department
They're not expressly forbidding that I know of but the rocks leading to the beach would not be very safe. The beaches at Pacific City and Neahkahnie both have access that does not include hazardous rocks. I have seen horses on both of these beaches. Christopher Gass is absolutely right, the State Parks folks are very helpful about any questions.
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