You refer to "private roads open to public use."  While any private road can be used by public emergency vehicles in the course of an emergency, and by invitees of the owners of the private road, (such as their guests or delivery services,) private roads are not open to general public use unless they are also designated as a "public easement."  Roads that used to be town or county ways but were discontinued after 1976 generally became public easements automatically at the time of discontinuance, and this means that they remain open to public use by foot or motor vehicle, but the public no longer provides any maintenance or snow removal.  If there are residents on such a road, often their only recourse to keep the road passable may be to form a road association - which is then forced to maintain the road for public use at private expense. 

The other way a private road (that never was a public road) could become open to the public is if the town and the owners of the private road go through a formal process to have the town accept the road as a public easement.  This has become accepted practice in recent years to circumvent the prohibition against using town funds on private roads.  By declaring the road to be a public easement, that creates a public purpose for the road and thereby allows the voters to authorize the Selectmen to use town equipment on private ways when they deem it in the best interest of the public for fire and police protection. 

But towns are not obligated to maintain public easements - they simply are not prohibited from using their equipment to keep emergency access open.  That generally means they agree to provide snow removal, but no summer maintenance.  (It's a bit of a sore point for those on discontinued roads who would rather the road was NOT open to the public because they are provided with NO assistance from the town whatever - yet the public gets to use the road freely.)  Do you happen to know if your road is in fact a public easement?  If so, then it may indeed be up to the public to determine the speed limit.  But if it is a private road with no public easement, I believe it would be up to the road association.  If that's the case, you could provide a margin of protection by posting the entry to the road "Private road - for the use of members and their guests only."