Well, I guess that's down to the 'fashions' at your barn.
By which I mean - any age can and should wear them if they are going to aid their riding. Some people prefer to wear short boots and chaps, some prefer long boots. It is my impression (through reading on this forum rather than through experience) that at some English riding Barns in the US there are a deal of 'rules and regulations' about who can wear what and when which are based on fashion or barn standards rather then on necessity.
If you can ride in them, wear them.
If you are going to be mucking out, don't wear them.
If you are going to feel self-conscious wearing them, then save them for a special day.
The problem with long boots of course is that they show up the dirt and scratches more
If you wear them, clean them.