For the most part people didn't ride horses to get around town (despite what Westerns depict). Horses were mostly used to pull carts moving goods around like trucks do today. The average city dweller walked or rode trams.

In England in the 1600s it was perfectly normal to get a hackney carriage around town. Boats for longer distances.

Until 1976 the law was still extant that they had to keep a bale of hay in the vehicle.

The prices were even regulated

http://www.londonancestor.com/stow/stow-hack.htm

Indeed the Romans even had regulations about road width to ensure drawn carts could pass each other

https://en.m.wikipedia.org/wiki/Roman_roads

Even so, that's just using a cart and a hired one at that. I mean the analogy of a horse to a car (as in something you owned personally and rode around on) was never really true, at least in cities. Also, speaking of London, the Underground is surprisingly old -- the first parts of the system opened in 1863. Yes, Sherlock Holmes is often depicted as going by hackney, but had he really existed, he could have ridden the Tube.

What do you find so terrifying about individuals having the liberty to move around?

> he could have ridden the Tube.

But he took a carriage more often than not.

Yep, and 19th century American cities tend to have very wide streets due to horseshit. This is often misattributed to cars.