They make bags you can put on carrriage shafts to collect de poopoo. There is also a version for riding but would be more annoying since it's actually on the horse as opposed to the cart. They don't really pee while working but they do poop so that would solve the poop issue. Just a matter of dumping it somewhere appropriate. The main issue if large areas converted back to animal use in this regard would really be people adjusting to longer travel times and housing the animals. As they really do best on pasture as opposed to being stabled. City areas don't have good housing options for livestock, but the work itself is perfectly fine in terms of exertion.
It's interesting they never bring up Mackinac. It's an island where cars are banned and everyone uses either bikes or horses for transport. Emergency vehicles like ambulances are of course available though.