I’m in south-central Connecticut, which is not as cold as your neck of the woods, but I did use 4 layers of insulation on mine and it helped a lot. Where you are, you’re going to get even more cool days and I think it’s a necessity.
So yes, same amount of chicken wire, then at least two layers of stucco.
Do not compress the insulation under the chicken wire. The idea is to get a uniform shape, but to protect the insulation from compression. It’s not the insulation itself that keeps heat from escaping, but rather the air trapped inside the insulation. If you compress it, you are squeezing that air out and keeping it out, so it won’t perform nearly as well.
Many people like to finish their oven with a veneer, but it is not at all required. The biggest difference between the two is that you have to plan some time annually to renew the paint on the stucco to maintain a waterproof shell, so it is a little more maintenance. Personally, I decided to live with the stucco for a couple of years, and I actually like it now.