The address above is for the Manuel F. Correllus State Forest which forms the centerpiece of Martha's Vineyard's trails. Here's a link to it.
Correllus has a paved bike path that almost circumnavigates the forest as well as many single and doubletrack trails within it.
It is not well known but Martha's Vineyard actually has over 200 miles of public trails on protected lands. Theres are curated by the Sheriffs Meadow Foundation. Check out their website for more information on the Island's trails. They feature the TrailsMV ap. Which one can download into a phone or a gps device. It will show you the exposition you are at while out on the trails.
Riding on the island is a lot of fun. The trails are scenic, and often unexpeced given the development on the island. There are great ocean views as well as cool, quiet forest trails.
People ride here all year long. Given the soil characteristics mud is rare. As is snow, which doesn't last very long when there is any.
Riding in the winter, early spring or fall is especially fun as the summer's crowds are largely absent.
To get ther you'll need to take a ferry. Check the Steamship Authority for details. You can make a reservation for your vehicle or, park in one of the many mainland parking lots and ride your bike to the ferry. If you choose to leave your car on the mainland you'll probably not need a reservation.
Needless to say the Vinyard offers almost endless restaurant and lodging options.
The Vineyard Off Road Bicycle Association hosts weekly rides. Many trails are also featured on this Hotel's Website. Lastly here's a Martha's Vineyard Magazine article describing the trails, it's a bit dated, there's a lot more trails now.
Whether you plan a day trip, or an extended stay, you'll find plenty of trails to keep you busy on Martha's Vineyard.