Hupmobile photo from the National Archives

I came across this while searching for something else..

The driver is a chaplain, the passenger is a Brigadier General and presumably that is the rifle range in the background. There were very few cars in the Army this early.

That's certainly one of the first Army motorized vehicles.

Appears to be a 1911 from the high headlights and the slightly elongated running board (1909-10 running board was half that length, more of a step plate). No top nor windshield. I would say that this vehicle was the equivalent in usage of a golf car now, something to transport the Brigadier General around the grounds to inspect the troops, not something you'd drive into battle! And the fields must have been muddy, not the chains on the rear tires.......nothing looks shiny on the car either, for example the hood former on a production car was polished aluminum, as was the steering wheel hub and spokes....not so in this picture...

I think its more likely the Chaplain's car. A general would not have a chaplain for a driver and would have been very unlikely to have been able to drive himself. He would also have been mounted at this stage, regardless of his branch of service. The car is also painted "26th Infantry", meaning it belonged to a regiment. Regiments are commanded by colonels and the general was likely at least a brigade commander.

I expect the general is some sort of observer or referee in a field exercise. The enlisted men are looking very casual for being in the presence of a senior officer, unless they had orders to treat him as being invisible. Also, he's wearing an armband that says "executive officer". I'm not sure how that fits into the scenario but its definately not part of his uniform and would never be worn except for some sort of exercise. The first time an automobile was used by the Army was probably When General Leonard Wood used a White steamer to supervise the annual field maneuvers around 1908 (I don't have the exact date at hand). Near the end of 1909 the Army sponsored the "trans-continental dispatch car".... a 1910 Mitchell Model S that was driven coast to coast to deliver a dispatch. In that case, there was literally no one available in the Regular Army who knew how to drive so two volunteer drivers were found. Malcolm Parrott, who was actually a private in the NY National Guard, and Frank Zirbies, an employee of the Mitchell Company. Both wore regular army uniform, although Zirbies wasn't even in the National Guard.

Would the leather leggings on his legs indicate that he maybe came off a horse to take a ride in the car?

Not really... he would have been wearing them with that uniform as a matter of course, not just when riding. Prior to the introduction of mechanized transport it was expected that all officers and especially those above the rank of Captain, could ride. Field grade officers serving with troops had to be able to get around and the horse was the only practical way to do it. Most junior officers also rode and some, like the regimental adjutant, had to be able to. About the only place an officer might get away with not riding would be garrison duty in a costal fort or some sort of specialized staff function.