There are still a lot of people around using horses for work or pulling a wagon or carriage. I used several teams of draft horses for logging and pulling sleds for feeding and gathering firewood. I also trained saddle horses and pulling horses for myself and others. The countryside is covered with old horse drawn equipment, some still in usable condition, and some just good for parts. Same with harnesses. Many old barns still have harnesses, collars, hames, eveners etc hanging on the walls. Some are still usable and some would just make parts. There are people around that still make harnesses, saddles and horse drawn equipment. It would certainly be a slow process going back to using horse power in a large way, but many people do live in areas where the transition wouldn't be too difficult.
I still maintain that most people, in rural areas especially, are far more resourceful and adaptable than many people give them credit for. Those that aren't very resourceful or flexible, good riddance to them.