Babies have a very distinctive profile, particularly the way their nose turns up and the way the upper lip sticks out and up. The reason our noses stick up this way when we're born is so we can breastfeed and still breathe (or so I read somewhere). So these two qualities tend to give any character a more youthful quality, and are helpful features to emphasize when you're drawing people and you want them to look young.
As we all know, full lips and an upturned nose are considered classic beautiful attributes on women. I assume it's because (in our minds) those things equate youthfulness. It seems to me that many people (especially females) retain the upturned nose and full lips well into their teens and even into their twenties, thirties and beyond, depending on the genetics of the person.
The overall consensus seems to be that, yes, our noses and ears (which are cartilage) keep growing our whole lives (unlike bones, which stop at some point).
So drawing larger ears and noses definitely make a character look older.
Also, gravity begins to have an effect on our noses as well. At some point, the upturned nose begins to droop downward and the upturned cute nose disappears, replaced by the lower hanging, larger nose of an adult or older person.
Another thing that happens as we age is that our lips pull inward and lose their plumpness. They don't jut out so far anymore. If anything, the opposite happens, and the line of our mouth becomes more concave...
...particularly as we lose teeth and there's nothing to push them outwards anymore. And we lose that baby fat that made our cheeks so chubby. We can begin to look gaunt, with our cheeks sucking in instead of expanding out like they did when we were younger. They can sink in so far that you can see the cheekbones and other planes of the skull underneath.
All images from corbis.com