I don’t particularly buy in to the “horses are the devil” bandwagon some folk have hitched* themselves to, but I’ve also not been surprise mount-murdered by anyone (yet), and I imagine it’d be fairly frustrating.
So pitching a fairly simple suggestion to give pedestrians fair warning; increase the radius of the in-game mic indicator (which for me on PS4, seems to show even when muted, unless I’m in a Party) for mounted players.
Sidenote: the ‘being in a party turns you into a ninja’ thing might need to be addressed separately.
In fact, re-use of the voice indicator by sheer proximity (again, increased for mounted players, and perhaps dampened on foot via points in Agility) might be a better way to pull off the idea.
*see what I did there?