Don't wear white gloves for schooling.
Brown tack is out of fashion in dressage. Some people have been saying it's making a comeback for years now but I haven't seen it. So if you're in the market for a secondhand dressage saddle, a brown one can usually be had for less than an identical version in black. Different nosebands, browbands, padding colours are in fashion at different times - dropped nosebands are considered a bit old fashioned where I am, as are black bridles with white padding.
Brown boots are generally for schooling and clinics only, although some people are getting more adventurous with colours for showing.
At some barns, both dressage and hunter/jumper, you are expected to wear polo shirts and belts all the time while others are super casual and you can pretty much roll out of bed in your pajamas. Some barns, like mine, expect you to use only white or black saddle pads and boots/wraps. Hunters tend to go more crazy with their colours from what I have seen, although there are certainly dressage riders with wild colour combinations. Brands and fashion *in general* seem to be a bigger deal among hunters while I would have no idea what brand of breeches or coats or boots my stablemates wear except for the fact that we give each other recommendations for things to buy or do group orders from Calevo sometimes. Not that there aren't brand crazy people in dressage, but it's nothing like I have seen in hunter/jumpers where fashion trends seem to move faster and to take hold fiercely.
Everyone's first priority is riding at my barn, but we spend so much time together and it is natural to become close. It is a little bit of a club. We watch each other's lessons, which can be a great way to support each other and also learn outside of your own lesson. However, sitting in on lessons is discouraged at some barns and some people don't like having other people watch them ride. We also travel to shows just to watch our stablemates compete.