From what I see, that region is not that cold. However, the parts of your body that will suffer the more from cold are feet, hand, hear and nose, so it's better to properly cover these spot.
You just don't want to have cold feets, that break all the fun, so just get warm boots. I do not know what you mean by "full-on winter boots", but you are not going to the arctic after all.
Small tip, bring extra sock, change if your sock get wet. Wet sock and cold is the best thing to have frozen feets.
I went to Zao two times. One time I snowshoed, so you need real boots for that. The other time I took the snowmobiles up to see the snow monsters and just had hiking boots as we didn't walk through deep snow. It was really cold and windy on top of the mountain so I recommend a thick coat, hat, and good gloves. If it's a warm and sunny day it will feel pleasant but I wasn't so lucky.