Do you lose tleast some pairs of mittens and cap in winter

This is the perrenial problem in cold climates. You can buy mitten clips that you clip on the mitten so the little kid will not lose them. They come in two varieties: the short one you get two and you have a clip on each end, one for the mitten and one to attach to the coat cuff. The other long one has clips on each end and you put this up one arm, across back and down the other inside the coat and attach to each mitten. As to hats, I guess that was how hoods became popular. You might get a hooded jacket and then use a hat and use the hood as backup.