Looks like there are some public roads, and then some additional 4x4 only roads, but they are reserved for folks with disabilities and require a permit.
Doesn't look like there is any legal and approved wheeling in the area. It's mostly for mountain biking, hiking, horses, hunting, etc.
From the website:
Taconic-Hereford has two roads that serve as Motorized Access Permit for People With Disabilities (MAPPWD) trails. Permit holders can use a permitted vehicle to travel beyond the reach of public roads, to areas where others must hike or bike. The permit provides access for those who seek solitude, connection to nature, undisturbed wildlife habitat, and inclusion with fellow sportspeople. The 0.88-mile Brockway Road and the 1.24-mile TSP Road are both open for use with 4-wheel drive trucks and SUVs by people with disabilities to allow for wildlife viewing. This use is allowed seasonally during hunting season only, from 10/1 through 12/31. These roads are gated so users must contact the regional office in advance to get the lock combination or pick up a key for the gates.