Yes, subject to Massachusetts state hunting seasons and licensing; the forest is popular with hunters, unlike the more developed, day-use Clarksburg State Park nearby.
Can I bring my dog to Clarksburg State Forest?
Allowed caged, bridled, or on a leash or tether no longer than ten feet, unless an area is posted otherwise; never unattended or at large, and waste must be carried out. Hunting, hunting-dog training, dog sledding, sled-dog training and search-dog training are excepted (302 CMR 12.13).