Beating someone is never the answer to any problem. It just tends to create more violence and stupid vengeance. The best thing to do (the hardest and the bravest) is to try and integrate all of you as a group and be friends. You′ll have great memories as you get older trust me.
I'll just pop in here to refute your beating someone is never the answer. I only threw 2 punches in my school career, so I'm not sure if they count as beatings.
1) I was in 4th grade, at a family wedding. Another kid was picking on me, so my dad said to make him stop. I popped him, and he didn't bother me. At least that's the family story; I don't remember much of it.
2) A couple kids were picking on me in my first year at high school. Sticks and stones, flipping my collar on my shirt, etc. I got sick of it. The taller of the pair was walking towards me in the crowded hallway between classes. We made eye contact, he started smirking, and I put him on his knees with a good punch to the solar plexus as we passed - I kept on walking. Never bothered me again. :shrug:
Yes, it's a double-edged sword, but it can work. Like I said, just to refute your blanket answer. No offense meant.
Now, I've been punched a few times after school career. What I've found is that the person who threw the first punch usually ends up looking like a fool. Not due to my fighting technique, but due to me being able to prove my point in words that they will feel like fool for losing their temper, or not dropping me, and kind of processing the moment on the spot.
Regarding teacher involvemnt, there are typically procedures that they follow regarding incident reports, discussing things with the teaching team, and making counselors and admin aware of the situation. I've seen student schedules changed, teachers keeping a subtle eye on the situation and not letting the victim out of site, creating extra work for the bullies to keep them busy, etc. If violence breaks out, then the police are called and the attacker now has a record, suspension, or expulsion.
At the OP:
Going with Kid A on the slopes could be a good idea, and too late to sign up shouldn't be a real problem unless it's bussing logistics or the like. Just approach the teacher in charge for that trip, explain the circumstances, and see what happens. However, this won't help the long term. You should report what you see happening.