The Pine Barrens are pretty darn big, any particular portion of the Pine Barrens you were looking to go?
The best place to go would be Wharton State Forest. The Rangers there have been working to mark those areas that are off-limits. Wharton can get very wet though.
The best stuff in Lebanon State Forest is off-limits. You can still drive the fire roads, but the rutted hills and big mud holes are off-limits, $1000 fine plus 3x the amount of damage the rangers estimate you did to the land.
-Michael