I often complain about people who mistakenly consider pre-20th-century humans to be far less sophisticated than they actually were, and I may become guilty of that myself, but here goes anyway…
The Doppler effect will change the perceived pitch of a sound. People might notice a change, but ascribe it to a change in volume, not realizing that both the volume and pitch are changing. The horses feet, for example, make a combination of sounds, and I think that the change in volume might be so overwhelming that it might be difficult for ANYone to notice the change in pitch. The sound of the locomotive might be a similar sort of white noise which Doppler might not change to a noticeable degree.
None of the above would apply to the train’s whistle, though.
Yes, but not MUCH before.
According to Wikipedia, Doppler first proposed his hypothesis in 1842 regarding light waves, and it was confirmed in 1845 regarding sound waves. I’m genuinely surprised that sound did not come first.