Years ago and friend and I would do carriage rides for a guy we knew. We wore white long sleeved shirts, black slacks, shoes, vest and top hat and a ribbon type tie. I don't have any pics. We used a team of percherons. He had a wedding carriage and a pretty blue one also the team looked sharp and I must say we did too..
You do look nicely put together. Everyone has great suggestions so far. Here is my suggestion from the picture.
If the jacket buttons up, do it up. It would look great and complete a nice balance from the tan breeches and white shirt. Add a pair of gloves and you'd look super.
When I did tours for my local town, I wore a nice blue shirt, hair pulled back, my tan breeches, and black half chaps. I did this on the quiet days with my trainer to "learn the ropes". One day we did both carriage rides and pony rides. We both wore nice white shirts and black pants.