Unless you have snowshoes or cross country skis, the snow is too deep for regular walking. You'll sink into this soft snow. Best bet is to walk on the paths left by snowmobile tracks....that works pretty good.
For thin ice anxiety, have a couple Sam Adams beers, and you'll be good to go...lol
...just kidding. For thin ice anxiety, maybe a pfd, and two of those orange ice safety picks designed to claw yourself up and out of icy water, fast.
Apparently, ten inches+ of hard ice is enough for snowmobiles and atv's but not for cars & pickups. A snowmobile and driver & passenger can weigh up to 1000 lbs, and a car can weigh 4000 lbs.
The Meredith Police & Fire just got on track with two new snowmobiles, so's I expect to be seeing them, out & about the Meredith islands.