Yes, I think the idea of the cavalry as inherently snobbish is probably restricted to a few 'fashionable' regiments. The rising master of the 12th was British; again, having studied one regiment in detail I couldn't say whether that was typical or unusual.
A digression, since you mention Robertson as the first man to go from private to field marshal; does anyone have any idea who the first man to make general officer after starting in the ranks was? Evidently Robertson did so on his way to field marshal, but I'm guessing that there were others before him?