If you want to show, this is something you will have to deal with, and it’s better to start early. You will not be able to avoid the warm-up at your first (rated) show, as you are required to warm-up in designated warm-up areas. Not warming up at all will not help you or your horse with nerves at the show. I used to hate the warm-up, but with time and confidence-building from my coach, I’ve gotten much more comfortable, and have even introduced a totally green horse to showing. Neither of us died.
Skills you need to ride in a warm-up: emotional control, observational attitude (head on a swivel: LOOK UP ALL THE TIME), quick reflexes. All of these can be trained.
You can start by maybe trailering to a friendly barn where multiple people ride in the arena at once. Go with the only expectation of calmly walking around - maybe a little trotting. Use this first time to get comfortable with calling your lines (“rail”, “diagonal”, “outside”, “inside”, “circle”). Your only expectation is to experience it. Then… do it again. And again. Till it feels comfortable.
Go as a non-compete to the show. Just ride in the warm-up. Do this a few times until you are comfortable navigating around horses. Then, enter a class. In fact, enter two, maybe Intro A and B, so you get to experience the warm-up and show-ring transition twice.
Another rule about any crowded arena: the greenest horse gets the right of way. An upper level horse can easily be maneuvered - if you can’t, you’re doing it wrong. A training-level horse or a 4 y/o cannot. Yield to the greenies.
ETA: And for the love of God, yield to horses having obvious difficulties. I took the afore-mentioned greenie to her first little schooling show. It was distracting and scary in the warm-up for her, and we lost a little forward momentum. The warm-up was HUGE, so I picked what I thought was a quieter corner, and carved out my circle and called it. Someone decided to extended trot right through it. My mare froze, thinking that Extended Trotter was charging her, and then panicked, going every way but forward. I lost control of the shoulders, and I did not want to pivot her hindquarters into Extended Trotter’s line of travel: egads. Extended Trotter was not yielding. I started yelling “You need to yield, she is green, you need to yield!” She didn’t. My warm-up was filmed and looking at the tape it was obvious that my horse was in trouble. And yet, we got bowled over. I was livid.