The most crucial piece of gear would have to be your boots - hiking boots, even insulated ones, do not usually stand up to the cold when you are standing still. A boot which is taller protects your feet from getting wet. Look for a boot designed for winter, and take note of how thick the sole & liners are - the thicker the insulation the warmer the feet!  Rain boots are not recommended as they do not have enough insulation.

 

Hats and gloves are the next priority - waterproof & windproof (nylon or canvas type) are the preferred materials since your hands will most likely come in contact with snow at some point, and your head is where you lose most of your body heat on a cold day.  Children in particular should have warm hats and gloves. Look for a wind/waterproof outer layer with a fleece/thermal inner layer. 'Gore-tex' is a great example.

Snow pants and a winter coat  - should have similar properties as described for hats and gloves. Waterproof and windproof are recommended. 'Gore-Tex' is an easy to find product which is very effective. Less expensive synthetic gear, that is designed for winter, works well when you use the layering approach.

Clothing next to your skin  should be made of synthetic fibers such as nylon, polyester, or rayon.  Cotton has NO insulating value!! The layers between you and your waterproof outer layer will also hold your body heat more effectively if you add a fleece or wool layer. These layers can be combined in many ways to suite the temperature of the day.