IIRC in some of the Fire Emblem games, characters that had mounts had a different movement mechanic, being allowed to move both before and after an attack, instead of just before like ground-based units. Probably not quite the same thing as what you're thinking though.You know, this has me thinking that it would be interesting in a turn-based RPG for a mount to have some sort of combat function if you were riding it and a battle occurred. I'm not sure if I've played a game with such a thing.
^ I seem to recall it being the same in FFVII. Maybe VIII let you skip entirely (iirc the rental cars did). Hmmm. Time to break out the PS2?
In Final Fantasy Tactics, if you have an allied chocobo on the field, one of your units can ride it. Chocobos usually have far superior Move/Jump stats compared to units on foot (Black Chocobos can even fly), but the chocobo can't act separately from its rider.
In FFXIII, while you avoid battles while riding a chocobo, getting close enough to a monster to normally cause a battle reduces the chocobo's "morale" meter, and running out of morale causes the chocobo to throw you off and run away.
Red Dead Redemption had gunfights while walking and horseback. Not RPG, but it was very well done.
In Dragon Age Inquisition you can ride horses and the enemies will start attacking you as normal, and you can't fight back (or your companions, since they disappear when you mount) until you dismount. And they made the game very slow on my PS3. I nicknamed my horse Laggard.
I forgot to mention Tactics, though it's my favorite game.
I didn't know that about FFXIII. Though I got stuck right before the final dungeon like a dork.
In fairness, quite often you can't do this with the unmounted player-character either. To take Red Dead Redemption as an example, the logical control for 'walk backwards' would be to pull down on the stick. Both man and horse turn around rather than walk backwards when you do this. And left and right on the stick turn both, rather than side-stepping.2. Their maneuverability is awful. My real life horses can back out of a tight corner, or step sideways. Hell, they can go sideways awfully fast to get out of the way of a threat. Why can't video game mounts do all that?