One of the TV shows "Best of America on Horseback" had riding on the Outer Banks. They recommended riding on the beach near the Bodie Island lighthouse. This would be in the area included in the Cape Hatteras National Seashore. There is a parking lot which has enough room for the trailers, and bathrooms for the people.
According to the NPS website:
Horses: Horses may be ridden only on the ocean beach seaward of the existing dunes, on vehicular beach access routes, along road shoulders or directly across paved routes where travel is necessary to cross to or from beach or beach access routes
The TV show also said that riding on the beach was not allowed in the summer. The people participating in the program brought their own horses and staged at Elizabeth City NC.
Equipment: The trailers came from Elizabeth City via route 158. They recommended bringing plenty of water to hydrate the horses well, and being sure that the horses were fit, because riding on the sand is harder on their legs and hooves. You also have to have a good way to wash all the salt off the horses
When my kids rode horses in the water, they often rode bareback, because water is hard on the leather in the saddles, and salt water even moreso. If that isn't an option that you are comfortable with, either stay out of the deeper water/waves, or ride with a bareback pad or something similar. They also used web bridles instead of leather ones.
This is a sign at the base of the Oregon Inlet bridge which explains about the U.S.S. Dionysus which was sunk to provide an artifical reef for a fish habitat. The sign says:
"One of four World War II Navy Liberty (transport) ships purchased by North Carolina, the Dionysus is now part of the State's Artificial Reef Program. Prior to submergence, this case bronze 11-ton propeller was removed for display."
Liberty Ships were emergency built ships which it was intended would be only for short term use during the war. Henry Kaiser developed the time-saving "prefab" method of shipbuilding. This allowed a liberty ship to be assembled from parts constructed off-site, using labor unskilled in shipbuilding techniques. As a result, the liberty ships were completed much more quickly than was possible using the more traditional means. In one recording setting effort, the elapsed time from keel-laying to launch was 4 days 15 hours. The Dionysus was built by largest of the wartime emergency shipyards, the Bethlehem-Fairfield Shipyard in Baltimore, Maryland.
In 1978, her main engine was donated to the Mariner's Museum in Newport News, Virginia, where it is on display.
"Today the vessel lies under 80 feet of water, five miles southeast of here. Resting adjacent to 3 other Liberty ships, the Dionysus provides a recreational paradise for sport fishermen and divers."
Equipment: The diving depth is 65 feet. You can see several species of cold/cooler water marine life -- mussels and tautog -- on this wreck. When sunk as artificial reefs, most, if not all of the liberty ships were cut down to at least to the upper deck level, thus removing all of the superstructure and other "interest ing" parts. Others were cut down to only 15 feet above the keel.
This is billed as the home of the largest and most modern fishing fleet on the eastern seaboard. Listed are the boats
CAPT. B C
MISS OREGON INLET
Equipment: The NPS has a boat launch facility adjacent to and behind the Oregon Inlet Fishing Center with ample parking for cars and trailers. There is no fee for use of the facility. Bait, ice, fuel, oil, camping supplies, fishing tackle, boating equipment, clothing, food, beverages and printed copies of North Carolina fishing regulations are all available from the Oregon Inlet Fishing Center main store.
Fishing can be done in the islands but check before you go. Most tackle stores can inform you where it is legal to fish.