John B.
Yelp
People come for the horses, but even if you don't see any, you haven't wasted your day by any means. I learned on my last visit that there had been previous efforts to develop the island into a human-rather than equine-settlement. This failed, which seems for the best, as the island is narrow, swampy, and subject to storms. It makes a great place to visit but I wouldn't want to live there.
It is possible to not see horses (though you'll definitely see what they've left on the road), but I was fortunate enough to catch a team that was grazing directly under the nature trail boardwalk. They tell you to stay along way away from them due to the potential dangers, but the boardwalk was a perfect height that one could be much closer than the 40 feet they recommend if you were on solid ground, and made for great pictures. I saw a plaintive looking sika deer too. Don't skip the boardwalk is what I'm saying, though there are no guarantees.
The beach on the oceanside is wide open and some of the best you'll see in the Mid-Atlantic. Australia it ain't (believe me, I know), but the sand is clean, the breeze regular, and nothing manmade can be sighted in any direction.
There's a lot of general weirdness in how the whole park is set up. The initial land you reach upon driving over the bridge to the island is a state park, with separate entrance fees. The national seashore goes the length of the island, which is very long, but road access doesn't go that far. You can drive an hour inland to Chincoteague to access another stretch of the same beach. The day use fee is high, and a yearly park pass becomes a good deal. High fees are understandable though, as the big problem with Assateague is that the entire Baltimore-Washington Metro Area wants to go to this one little stretch of beach. During peak times, it's hard to get in due to the crowds. Once you're in, there's plenty of space, but I would either leave very early or go on an off-peak kind of day.