My dd was born with a ton of hair, too. It even made her look sort of like Winnona Ryder. People kept telling me that it would all fall out, but it didn't. Now, she is 18 months old and her hair is shoulder lenth. She wears either the classic pebbles or two pony tails.
And, I promise, there is no punishment involved in styling her hair. I have never even yelled at her, let alone punished her. Dh asks her each morning if she wants one pony tail or two and she tells him. After a bath she often runs around with her hair down and, the minute it is dry and in her eyes, she comes running up with a hair tie in hand and asks us to fix it.