Nice hearse...
It is a 'cut under' which means it could turn in tighter circles without tipping over. The whip socket is on the right side of the hearse, it is intricate work on the right side below the seat. In driving horse drawn vehicles the 'human driver' is on the right side, the assistant or 'groom' sits to the driver's left.
The roof is curved and those black box like notations on the roof, is for finials that would keep the flower bouquet frequently on top and covering the casket if there was no room in the hearse's body. Excess flowers, bouquets would ride on the roof. (Sort of like a roof rack) If it was sparse, rods with crape would box out the roof line. The carriage lamps (the headlights for the day) seem wrong for the design and proportions of the hearse to me...They should match the ornate whip socket as far as luxurious appointments...more delicate.
Still, its always a pleasure to see old horse drawn vehicles.
M. E. Wolf