Whenever hiking during winter, you face two challenges: staying warm and staying dry. To beat both, your best bet is to layer your clothes.
Wearing multiple layers of clothing will provide various levels of protection against sweat, heat loss, wind, and potentially snow (As often the case with kids, they love to tramp through and fall in it!). Layering works because the type of clothing you select for each stratum serves a different function, such as wicking moisture or shielding against wind. In addition, trapped air between each layer of clothing is warmed by the child’s body heat. Layers also can be added or taken off as needed.
First three layers
Generally, both you and a child need at least three layers and if really cold four layers. Closest to your skin is the wicking layer, such as long-sleeved synthetic material like polypropylene (This can be found as modern long underwear, both bottoms and tops), which pulls perspiration away from the body and into the next layer, where it evaporates. Exertion from walking means you will sweat and generate heat, even if the weather is cold.
The second layer is an insulation layer, which helps keep you warm. This layer probably also should cover the neck, which often is exposed to the elements. A turtleneck works fine, but preferably not one made of cotton, as this won’t wick moisture from the skin when you sweat.
The third layer is a water-resistant shell that protects you from rain, wind, snow and sleet. Depending on the temperature, could be a wool sweater, a half-zippered long sleeved fleece jacket, or a fleece vest. Any windbreaker worn should be breathable and water-resistant/waterproof.
Fourth layer
You also might even add a fourth layer of a hooded parka with pockets, made of material that can block wind and resist water. Gloves or mittens as well as a stocking cap or ski mask also are necessary on cold days.
For your feet, use a synthetic sock liner with a wool sock. This then can be covered with your hiking boots, to give your ankles the support they need when walking. Since you’ll be walking over and possibly through snow, wear winter boots over your hiking boots to keep them dry.
Finally, don’t forget sunglasses to prevent snow blindness.
Read more about day hiking with children in my Hikes with Tykes guidebooks.