Waltham got rid of their overnight parking ban as a trial in 2013 and then permanently a couple years later. They have a couple of ordinances that deal with snow removal and narrow streets that might be worth considering.
First, parking is prohibited when a snow emergency is declared or "upon the accumulation of 2 inches of snow". I am not sure that's an especially enforceable legal standard (Who measures? Where? How is it documented?), but otherwise setting an expectation that a given amount of accumulated snow is the standard for declaring a snow emergency and possible towing is possible.
In addition and unrelated to snow, Waltham also has the "10 ft rule", which forbids parking "less than 10 feet of the width of the roadway for the free movement of vehicular traffic or in such position as to block the driveway entrance to any abutting property". It's a towable offense. I think that might be something for Newton to discuss.
Learning more about what happened in Waltham, which has dense residential properties similar to Nonantum and other parts of Newton, would be useful.
Relevant sections of Waltham regulations below.
--Mike
ARTICLE 5 STOPPING, STANDING, PARKING
Art. 5 Sec. 15
WEATHER EMERGENCY REGULATIONS
Whenever impending weather conditions threaten to constitute a traffic hazard impairing transportation, the movement of food and fuel supplies, medical care, fire, health and Police protection, and other vital facilities of the City, the Director of Consolidated Public Works shall declare an emergency period.
Whenever such emergency exists, and the Director of Consolidated Public Works shall have caused announcement thereof by the use of available news media, any or all of the following parking prohibitions shall become effective at either the time designated or upon the accumulation of 2 inches of snow in absence of a declaration. Permit B-3252 12/77. Parking on any street shall be in violation of this section. (TC 4/03)
No driver shall stop, stand or park any vehicle on any way, provided, however, that this regulation shall not apply to passenger vehicles stopped temporarily during the actual receiving or discharging of passengers nor to commercial vehicles lawfully stopped temporarily during the actual receiving or discharging of passengers nor to commercial vehicles stopped temporarily during the actual loading or unloading of materials.
Art. 5 Sec. 1
WHERE PROHIBITED – GENERALLY
...
(18) Within 30 feet of an intersection;
(19) Within 20 feet of a crosswalk on the side from which traffic approaches, when properly sign posted;
(20) Within 30 feet upon the approach to any flashing signal, stop sign or traffic control signal located at the side of a roadway, when properly sign posted;
(21) Upon or within an alley or private way in such a manner or under such conditions as to leave available less than 10 feet of the width of the roadway for the free movement of vehicular traffic or in such position as to block the driveway entrance to any abutting property;
(22) In any street or part thereof where signs have been placed for the purpose of facilitating the cleaning of streets, the maintenance of streets, the plowing of snow or the removal of snow.
Art. 9 Sec. 5 GENERAL PROHIBITION TOWING ZONES
(Says that the above offenses can result in towing.)