I can relate man. I literally cried about this fear two weeks before I came home. I had a panic attack about it (well and some other stress). It got really bad.
I am out to my family but they're bad with name/pronouns. And I will have to come out to my grandma this Christmas because I'm seeing her when I come home after second semester, and by then the changes will be too far for me to really hide it. I can't get out of seeing her either- it's a family vacation we always do that I was going to miss, so they're rescheduling the entire thing around when I come home. I'm SO anxious because she's paying for a part of my college. (I think you said you looked at SCAD? Or maybe it was another guy I honestly can't remember. If you did I'm sure you remember that its darn expensive, so this money is important.) She's a great and supportive person, BUT she's also super Republican, verging on Tea Party-ist. She isn't very religious (they say grace before family meals but they only go to church on like Christmas sometimes) so I am not worried about a religious argument, but I am still worried by the fact that she's generally very conservative. She watches fox news and I know that they are NOT trans-friendly at all.
Anyways I was just going to say that back at college everyone calls me Dean and he and I've got SO many supportive people, but here people flip flop and sometimes people don't even know so they use female pronouns and my old name. It's hard. I was expecting to come home to all female pronouns actually, because my family NEVER got it right before I left home, but I was pleasantly surprised. They're not at all good at it, they usually mess up, but they're definitely showing more effort. I don't know how you feel about this idea, but perhaps you can come out to them later during break and give them time away from you during second semester to think about it, but also make it clear you're starting T? You could also come out at the beginning of break if that's what you want to get your letter. That somehow worked for me- they seem ready now to try to use the right name and pronouns and I blame it on the fact that they've had time to think and I've proven that this is what I'm doing, I am willing to give my own money for this. My mom even pays for my T now. (I started T a week before going to college.) In my situation, the time away from home where I was being an adult and making my own choices really helped them to understand that this is who I am and I'm going to lead this life whether or not they like/understand it.
You can also encourage them to go to PFLAG meetings in your area if you have them. My friend's parents were very uncertain for a long time but PFLAG helped them, and now I'm convincing my mom to go because it is people in the same situation as her that she can talk to for advice or help understanding. Those people will help her, but they will ALSO correct her on pronouns and encourage her to use my preferred name. It benefits you both really, she understands better and you end up with a more supportive family.