I took my 5-year old to FanExpo last summer where he dressed up as Captain America. Five months before that he cosplayed as Fire Nation Aang at an Anime North preview event held at our local library. Next FanExpo he wants to wear the Jawa costume I made him. He loves it.
The only reason a minimum age gets mentioned, from what I recall, is that if you're 13 or under you need to be with an adult. People can "be all weird and have fun" at any age, though.