There is a limited amount of parking at the top North Hudson Ferry Landing boat launch. From what I saw, it filled up pretty early. So people were driving onto the ice and parking along the shore. There are ‘no parking’ signs all around the boat launch, nobody seemed willing to tempt fate with the chance of being ticketed/towed. Also for what it’s worth, North Hudson streets are legal 4 wheeler trails (posted when you come into town).
The Bayport side may be a better option for parking, a lot more space over there and with a wheeler you can just drive on the ice from Lakeside Park. I cant comment on the legality of driving a wheeler around in that park, but there are tracks from them so other people are doing it.
Good Luck!