The rural population was indeed a significant source of demand for cars. From 1911 to 1920 the number of automobiles owned by farmers increased 21 times, while overall registrations increased 13 times. By 1920, more than a quarter of cars were owned by farmers. Rural doctors were also heavy buyers of cars, as they could serve a wider area, respond to calls more quickly, stay with the patient for longer without having to care for a horse. Rural postmen also used cars, as they could then deliver the goods that people were buying from catalogues.
The Model T in particular promoted rural use. It had high ground clearance, so it could clear the ruts on rural roads. It was powerful, with a top speed of somewhere around 40mph , and if you had a spare can of petrol, you could travel all day. Contrast that with the horse, which travelled at around 8 mph and had to be rested for a long time after around 25 miles.
As has already been mentioned by T.E.D. automobiles were considered to be much cleaner than horses. No manure and urine on the streets, which was a cause of fly-borne disease. The car was also considered to be the answer to congestion in urban areas, as a car took up less than half the roadspace of a horse and carriage. They were certainly convenient for those living in suburbs, away from the routes of the horsecars and streetcars of the day. Cars of course took no resource if you were not using them, whereas horses had to be fed and cared for whether they were ridden or not.
Most of the above comes from a couple of books. There is a chapter ‘Societal Impact of the Industry’ by Timothy F. Messer-Kruse in a book ‘The Industrial Revolution in America: Automobiles’ by Kevin Hillstrom and Laurie Collier Hillstrom. The second book is ‘The Automobile Age’ by James J Flink.