The Chincoteague National Wildlife Refuge is located on the Virginia side of Assateague Island and is very different from the Maryland side. First of all, you can't cross from the Maryland side to the Virginia side by car. That's because the Virginia side is totally dedicated to the preservation and care of the horses rather than tourists.
During tourist season, the horses are kept within the preserve. You can see them by booking a tour through the Chincoteague National Wildlife Refuge, where park rangers take you on a small open bus through the preserve to follow the herds. The fee is minimal and definitely worth the price.
If you prefer, you can walk along the beach or the many hiking trails and maybe catch a glimpse of the horses, but I would only recommend this for the most adventurous of souls. I did that on one trip and was confronted by an angry stallion trying to protect his herd.
There are numerous trails throughout the refuge on which to hike or bike and enjoy the wildlife. There are many species of waterfowl, herons, and egrets in the preserve, as wall as black squirrels and small Asian deer. A good camera with lots of film (or disk space) is a must.
I highly recommend bringing insect repellent and using it liberally, as bugs are definitely plentiful during the summer months.
The island itself is beautiful, a windswept barrier island that straddles the Virginia-Maryland border. The 14,000-acre refuge also includes land on neighboring islands, most of which are inaccessible to tourists.
The entry fee is $10 per vehicle, good for 7 consecutive days, and also covers admission to the adjoining National Seashore, another must-see.