All US citizens are perfectly free to travel on US roads and highways.
They can ride in the speed and comfort of a car, ride in the speed and comfort of a bus, ride a bicycle, and as far as I am aware, ride a horse or drive a horse and buggy, all without a license. They are also free to hitchhike, as long as they follow the applicable laws - again, without any license whatsoever.
They MAY NOT, however, operate the statistically single most-lethal weapon in the United States (the automobile) without appropriate training and qualification.
Riding a horse was a privilege of the nobility. The peons could walk.