Personally, I try my best to never wear a coat since they passed the rule circa 2018/2019 that you don’t have to wear one at all at training and below, but even at an unrecognized show, you may see most people stubbornly trying to cook themselves to death in a coat. I have a navy polo I usually wear that hides horse slobber pretty well.
For all three phases, I always find it helpful to walk up to the warm up steward when I get there, tell them my number so they’re not looking for me, and ask if they are running early, on time, or late. It just helps to get that out of the way and have a feel for timing your warmup. Your event is unrecognized, so it’s unlikely, but nonetheless possible they could have a bit/tack check (to make sure you have a legal bit, whip length, spur length, etc), so you should ask about that when you check in with the steward. Pelham isn’t legal. Snaffle is legal so long as it doesn’t have gag cheeks and the mouthpiece is not twisted, a Waterford, Dr. Bristol, etc. No boots, including bell boots, for dressage. If they are early in dressage or XC, you do NOT have to ride early (even if the steward tries to bully you into it), and may elect to ride at your assigned time. SJ times are a little more vague (they don’t even have to assign you one) and I really don’t feel confident with my grasp of the rules on that to advise you one way or another. Try to keep an eye on the action in the ring- the steward is there to tell you when it’s time for you to go over, but they’re volunteers and as a result sometimes they’re not very good at their jobs. In general, thank all your volunteers- eventing isn’t a cheap sport, but they’re a huge reason we’re able to keep costs relatively lower than other disciplines.
When going outside the dressage ring before my test, I also find it helpful to slow down to a walk or halt at the judge’s box/car and tell them my number, name, and horse’s name so we’re all on the same, correct page. If there are lots of rings close by, I also ask if they have a bell or whistle (so I don’t confuse my signal with the ring next door) and because I don’t have the best hearing, I also tell them that so they will usually be kind and ring me in when I’m near them and can hear it. You have 45 seconds to get into the arena after they ring the bell.
You may not have to deal with times on XC at the levels that your students are going, but despite having a coach who was AMAZING at introducing me to eventing, I will never forget my first ever event (recognized BN), where no one had explained optimum time vs speed fault vs time limit to me and I found out the hard way what they meant. The goal is to come across the finish between the speed fault and optimum times- lower than speed fault and you get penalties; higher than optimum and you get penalties. Time limit exists really only for those having an awful day- if you get lost on course, take the world’s most scenic detour, or have a nappy horse that wastes minutes not going in the box or having a fight about turning away from home, etc, they place a limit on how long you can be out on the course before calling it a day. Some riders may have a fancy Optimum Time watch (an atrociously large wrist stop watch), but a cheap Walmart watch with stopwatch function works fine for lower levels if you will be dealing with time. It’s also recommended to not bother with time at the lower levels- just go out and have fun!- but timing yourself can also be a helpful experience for developing a feel for pace.
Another note on XC times: your students may drop down to a trot or even a walk anywhere on course EXCEPT between the last jump and the finish. That type of obvious ploy to run down the clock when you’re too close to speed fault is called “willful delay” and can get you in trouble. You’re also welcome to circle anywhere on course to waste time or get your horse back under control, so long as you haven’t obviously presented your horse to a fence.
Also hailing back to my amazing first coach, I assume your students will be on super lesson horse types, but it can nonetheless be very comforting as a rider to get a lead from the ground in/around the start box. My coach’s first upper level horse was nappy about the box, so she always made sure to provide a ground lead for the first few events to make sure everyone got off on a positive note. When I’ve had leads, the ground person usually steps away when they either mark 30 seconds or do the 10 second count down.
Good luck and I hope your riders have fun!!