For the northern United States, winter as well as early spring and late autumn require cold-weather clothing.
Besides layering with thicker clothing or even adding a fourth layer, you’ll want to wear gloves or mittens. The latter is better for children as they keep the fingers grouped together and so warmer. Scarves or mufflers are needed to the cover neck.
Always bring extra shirts, socks and even shoes to change into after the hike. Shoes likely will get wet on a cold weather hike, and children will need new socks so they don’t have to suffer through cold feet on the drive home.
Read more about day hiking with children in my guidebook Hikes with Tykes.