If you were a child any time before the 1990s your memories of wearing wool might be similar to mine. Some of my earliest recollections of winters in Norway, involve me barreled up in course and scratchy wool base layers to keep me warm. Only years later did I discover how soft wool can be.
Keeping our kids warm outdoors is probably one of our main concerns as parents, but we tend to overlook the fact that we can actually make them 'too warm'. As a rule, kids tend to feel the heat more than adults. Above all, babies should not be dressed too warmly, because they transpire heavily.