Probably best to call the township, see what the details are, hard to say if you are open to any liability or not if you do so. Personally, I'd be inclined to do so carefully, don't create any hazards, like a blind area from a snow bank or similar.
Years ago, the town seemed to be a little slow and or our 1/4 mile lane would not get plowed, mind you the towns garage and complex is less than a mile away. Might have just been a period of time, not sure who the highway superintendent was then either. So I would have to plow our lane, which is a hill, so I could get my vehicle to the house, so 2 passes with the K10 and fisher snow plow worked great. It seemed for that time period, you never knew if the lane would be passable during a snow event, at certain times, usually after dark. Ironically, the current highway superintendent seems to take good interest in the roads and he will run one of the one ton pick ups with a plow and sander on these hilly roads. I have not had to plow the lane for many years, they either have people on after hours now or whatever the difference is, the job gets done on time. At the end of the lane, is a half a cul de sac so its not the easiest turn around. I try and help out and push the snow banks/piles much further back onto the lawns, give the truck driver lots more room on frozen ground. In the spring I run the tiller and take a wheel barrow, hand tools to repair where the sod gets peeled up or ruts are left. I'd rather do that, then call and complain, I think they do a great job, I always wave or say hello to the drivers, and help where ever I can. Can't please everyone, the guy who runs the blower on the skid steer, clearing the now 10 year old sidewalks is a miserable sort, they wait too long to clear it, it gets hard, then he b$tches to the town superintendent, who then calls the resident who is blamed for excess snow from the small lane between houses, a shared driveway, open on either end, that has a name on the tax map, its just not deeded to the town. Snow has to go somewhere, and I know our 3 pt blower would easily get through it. Happened last year, what an easy job, but some you can't please.