Any city or village may provide for the destruction and removal of specified portions of weeds and worthless vegetation within the right-of-way of all railroads within the corporate limits of such city or village and may require the owner or owners of such right-of-way to destroy and remove the weeds or vegetation from such right-of-way. If such owner or owners fail, neglect, or refuse, after ten days' written notice to remove the weeds or vegetation, such city or village, by its proper officers, shall destroy and remove the weeds or vegetation or cause the weeds or vegetation to be destroyed or removed and shall assess the cost thereof against such property as a special assessment. No city or village shall destroy or remove or otherwise treat such specified portions until after the time has passed in which the railroad company is required to destroy or remove such vegetation.