I had a Saddlebred, so we keep their tails up so they grow. It’s a saddlebred thing, not a driving thing. This horse grew A LOT of tail. I think about 6" got cut off at every show to keep it from getting caught in wheels. When I stopped showing him, it stopped getting cut. He was a sweetie, but a lousy show horse. The real shame was he loved horse shows.
ETA - It’s not uncommon to see the tails of school horses kept up like a show horse, just to grow a tail, especially if it’s a light color (expensive). Just another way to pay for schoolies.