Henry Hudson Drive is typically closed from mid-November through mid-April. When conditions permit, the roadways to Englewood and Alpine Boat Basin are kept open during that period, but the Drive from Alpine to Englewood and from Englewood to the southern park entrance in Fort Lee remain closed.
They post openings and closings on this page:
http://www.njpalisades.org/hours.htm
It may be possible to ride on the road anyway. Anybody know? The gate at the Englewood side was closed the other day, but one could climb over it easily.