The below is referring to the parking area just inside the main gate on the right side.
From the U.S. Fish and Wildlife Service:
Please be advised that this area is no longer open for parking. We
understand that over the years it has been used by members of the public
walking on the nearby Rail Trail/Track Road. However, this area was
never an official parking area, and was not intended to be used as such.
Recently, the Assabet River National Wildlife Refuge has completed
construction of a brand new parking area approximately 300 yards
further up the road. All visitors are encouraged to utilize this new
parking area.
While dogs are not permitted on the Assabet River National Wildlife
Refuge, visitors wishing to walk their dogs on the Rail Trail/Track Road
area are still welcome to park in the new lot. We only ask that you walk
your dog(s), on leash, directly back down White Pond Rd to the Rail
Trail/Track Road.
Please do not park on the sides of White Pond Rd. This road is already
very narrow, and doing so can hinder local residents, and other visitors.
It also impedes snow removal and emergency vehicle response. Vehicles
parked along White Pond Rd will be subject to fines and towing at the
owners expense.