No, the government didn't "stop the use of horses" as you say, but they were damn sure replaced by the automobile. Back then, people didn't think the new technology (gas powered engines and autos) would be able to replace what they already had (horses). However, when the technology got to a sufficient development point, people saw the usefulness of them, and replaced the horses themselves.
Same thing is going to happen with electric cars. When the tech gets good enough to equal or surpass gas engines (and it's damn near there, most EV's can go for over 200 miles on a single charge), people are going to start switching to electric. And, not only are electric vehicles quieter and more eco friendly than gas, but they can be much faster and have a hell of a lot better torque. Currently, if you want to win drag races, use an electric vehicle. Power is transferred to the wheels almost immediately, resulting in much faster acceleration.