I'm sure there are a lot of factors in your parents not wanting you to go. Your age is a big one, then there is the time of year (not a good time, even for Georgia), the distance you have to travel to get there and finally the expense of such a trip. And that is assuming you already have the proper gear to handle March weather in the Mountains, which can be bad.
I'm guessing you have a school break in March which is why you want to go then. Even so, you'd be best off waiting until summer and doing trips a bit closer to home for a few more years.