Great reminder as its usually a surprise to some folks.
Unless things have changed from past years, anyone parking in the road or on the paved shoulders during the storm is almost guaranteed to be towed. If its a long storm, the crews usually take a break at the end of the storm and then go out the day after the storm and wing back the bankings, cars parked on the pavement (or paved shoulders) are still subject to towing during this period. Once the clean up is done, generally folks parked along the road on the shoulder outside of the travel lanes are at far less risk of being towed. This usually works until the next weather event. Realistically barring a significant thaw, once the snow banks are established there really isn't an option of parking off the paved section of the road at many trailheads. The folks potentially impacted are those who go overnight or multiday trips, the road may be fine when you park but if a storm comes in or is even predicted, the state may tow preemptively. Individual plow drivers seem to have different styles, many if given time do a nice job opening up the parking near trailheads but if there is a car the way they cant do much.
Pine Bend Brook trail has a proper lot, its just 1/2 mile down the road at Sabbaday Brook trail. I always have been curious why a connector trail in the woods paralleling the road hasn't been put in place to cure this issue.