In a word, yes. Especially in the rural US. Farmers maintained many of the roads, and when they encountered automobiles it was often not a happy event. Early cars ( circa 1900) were noisy ( mufflers technology was not completely advanced) and unreliable. Automobiles could go faster than buggies, and the risks were therefore higher when they interacted. If you look at a typical day on Market St in San Francisco in 1906, you can see that there was a lot of mixing of all sorts of vehicles , pedestrians...at a relatively slow speed. When farmers had to share the roads with them, their horses and livestock could be spooked, and it was not unusual for a farmer to have to haul a broken automobile into town behind his mule. Automobile owners were also likely to be wealthier and urban. There were incidents of farmers attacking "devil wagons": shooting at chauffeurs, throwing rocks, and sabotaging their own roads with ditches and obstacles. Local laws were passed regulating automobiles reflected this fear. The most famous "Red Flag "law, which required that a driver disassemble the automobile and hide it in the bushes if a horse-drawn vehicle approached, and have someone walk in front of it waving a red flag, was never in fact passed. But laws requiring drivers to slow or stop in the presence of livestock or horse-drawn vehicles were passed, and counties in Pennsylvania and West Virginia tried to ban cars in 1908.

That began to change with the introduction of the Model T, circa 1909. Henry Ford had grown up on a farm, liked farmers, and because his Model T was reasonably light and had good ground clearance it worked pretty well on rural roads. It was also not that expensive, and farmers began to appreciate the usefulness of the Model T. They could be used as tractors, snowmobiles, and a source of power, similar to the steam traction engines, for driving equipment like threshing machines.

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