People who live in climates in which the winters are very harsh are all too aware of how difficult it can be to dress a child appropriately for playing outdoors in winter. The cold temperatures will quickly penetrate through clothing and unless a parent or caregiver knows how to compensate for that sort of thing, a child may be rather uncomfortable after not being outdoors for very long.
The specific type of coat, winter pants, hat and so forth isn't as important as creating a protective barrier that blocks the cold is. Ideally, layers will accomplish this.
*To protect the upper body:
Put an undershirt under the child's regular shirt. Ideally, a turtleneck will provide some good insulation and protect the neck, but few children are likely to be willing to wear a turtle neck. In any case, it is important that they wear a sweater that will protect them under the coat. Buy or make a fleece collar that will go over the head. these can be a great way to keep a child's neck warm, and the soft fleece will be appealing to a child.
*To protect the head and neck -
Children will probably balk at the idea of wearing a scarf and hat. If possible, purchase a ski type mask that covers the head and neck and leaves the eyes and mouth exposed. These are usually made for men and boys. You don't have to resort to wool to keep a child's head warm. Chances are, they will find it itchy anyway and won't want to wear it. Make sure that the hat is soft and comfortable to wear.
A hat that covers the ears is also essential. Make sure that the hat fits snugly or it will fall off too easily. If the child will accept the type of hat that has ear flaps and that can be tied under the neck, that's a great option. If the child's jacket or snow suit has a hood, the hood will provide added protection and should be used.
*To protect the lower body -
Sweat pants or thermal undies that are worn under regular pants are both good options. Remember, the layers can't be so constricting that the child can't move properly. Snow pants that are insulated are ideal to wear over pants and will allow the child some protection from both the cold and wetness.
*To protect the hands -
Mittens are the best protection for a child's hands. It is important that the mittens fit properly and that they have some sort of elastic closure at the wrist. That will keep the warmth in. Ideally, the mittens will have some extra fabric above the wrist that can be tucked under the wrist part of the jacket sleeve to keep the cold out even more.
Thinsulate or other thermal protective products are quite good at holding heat in. Make sure that the child can move his or her hands in the mittens. If it becomes difficult to make or throw a snow ball or do other things that kids typically do outside, a child will likely take off their mittens without thinking about the consequences.
Some bright and colorful mittens or gloves will be more appealing for a child to wear. Consider getting mitten clips or mittens on a string. The long string will make it possible for the mittens to go from one sleeve all the way over to the bottom of the next sleeve. This will mean that the child won't have to be so worried about losing their mittens or gloves.
*To protect the feet.
Boots are the ultimate protection for feet. They must be waterproof, and they must have some sort of insulation inside. They should also be half a size larger than the child's regular shoe to accommodate socks and foot movement. Make sure that the boots have proper traction for walking and running on snow and ice. They should be easy for a child to put on and take off all by themselves.
Children probably won't be willing to consider wearing sock liners. If that's the case, look for some fun socks that are sure to keep their feet warm. Socks with separate toes in funky colors might be really appealing. Fleece socks are soft and fuzzy and kids will love them.
The key to keeping a child warm is knowing what they will wear without making a huge fuss. Children will battle with their parents about the stuff they wear. They like to have fun clothing. Outerwear that is brightly colored, that has all sorts of cool pockets or secret compartments will be big winners with kids. Add to the cool factor by putting some really fancy zipper pulls on their jackets and boots. In the end, when children discover that their outerwear will really keep them warm and that it can look cool and be fun to wear, any difficulty you might have had about bundling them up will resolve itself.