For training purposes, everyone in the barn that I can think of wears them. It’s bright here! Most of us have some kind of bluetooth sunglass so we can have easy two-way communication with our trainer without having to shriek at one another. I have Lucyd Lytes (they were a lot less expensive than the Bose ones and they weigh nothing.)
Dear Horse got spooked by something the other day when I was leading him. I didn’t let go fast enough and he span me through the air, I landed hard, face first and downhill, and plowed a furrow through the gravel with the helmet brim and nose. Glasses didn’t budge and were unscathed and damage to my face was minimal. (I can’t say the same for the rest of my body which was road rash central, and my right shoulder hates me again. And I had a hole in the knee of my breeches. Go large or go home…)
I wouldn’t wear them in the show ring as the communication part would certainly be illegal, but I do wear regular sunnies. No-one cares, truly. All the judges I know would much rather you be comfortable and focused so you could ride your best.