Answer:
Generally speaking, yes. The land and the gate are under the control of the roperty owner.
EXCEPTION: When the private road is also a legal established 'right-of-way' used to access otherwise 'land-locked' property belong to someone else, the roadway should remain passable at all times, OR the landlocked property owner should be provided with a key to allow him access to his property.
Other than this exception there is no requirement that a property owner offer access to his road to the general public.
A Different Perspective
You cannot gate and lock a private road if others are entitled to use it. private ways and rights of way are complicated areas of law. In most jurisdictions and in most cases a comprehensive title examination must be performed to reveal any existing rights. You should consult with the attorney who represented you at your closing to determine what rights may exist in that road. Your attorney should have a copy of the title examination.