Whenever any highway becomes blocked with snow to an extent that renders the same impassable for public travel, the selectmen of the town in which such highway is located shall cause such highway to be opened for public travel at the expense of such town within a reasonable time thereafter, if they find the same to be required for public convenience and necessity. Any selectman who fails to open any highway so blocked, when requested in writing so to do by six taxpayers residing on or near such highway, shall be fined ten dollars. The provisions of this section shall not apply to any highway within the limits of any city or borough, unless the town has the supervision of the highways in such city or borough.