Yes, before 1900 there were a number of what's called Red Flag Laws, which required a pedestrian to walk a distance in front of the car with a red flag, or lantern. The concern ( which was pretty valid) was that the car would alarm horses, and horse-drawn traffic was mostly what would be found on the roads before 1910.

The most extreme ( possibly most fun) example was one crafted by the Pennsylvania legislature in 1898 that would have required automobile owners to actually disassemble and hide their cars in the bushes when a horse drawn vehicle approached. (It was vetoed by the governor, alas). After 1907 and the introduction of the Model T, cars became common and the horse-drawn vehicles were the ones having to take precautions.

Absolutely they were.

For example, in my hometown of Queenstown in New Zealand, a local ordinance was enacted which banned motor cars from using Frankton Road (the quickest and most direct route into Queenstown) under the excuse that the noise of the motor cars would frighten horses. Motorists were forced to take the much longer, much rougher back roads.

It was only the increase in the tourism trade in the 1920's that forced the council to overturn the law.

What really terrified people were the steam driven trucks like the Atkinson Steam Wagon. Until the development and widespread use of larger petrol driven engines, steam was the primary method for transporting heavy loads, like petrol. This lead to some steam wagons catching fire and exploding with their loads. It was actually very uncommon, but common enough for many cities and local governments to ban steam wagons in the city and from using tunnels.

Our Motoring Heritage, T.T.N Coleridge.