Requires Mixin Booter and Elegant Networking to function.

What this mod does:

Horses will no longer always face the direction the player is, instead they will face the direction they are moving.
Horses can no longer change direction instantly (unless configured to), and will rotate to their intended direction over time.
Gives horses very light acceleration so they feel less jarring / more smooth.
Allows horses to sprint, increasing their speed but making them turn a lot slower.
Allows non-undead horses to swim in water, and water will no longer dismount the player.
Removes rearing / the horse randomly halting all movement at times.
Wild horse stats (HP, jump, and speed) distribution, min, and max values are now configurable.
Breeding now takes the average of the parents with a +/- modifier up to a cap instead of the average with a third totally random horse's stats (configurable).
Horse hitboxes are a bit smaller (still roughly the same space requirements)
Leaning mechanics while on a horse - When the player is looking down over the edge of a horse, they'll lean over for a better view.
Drawing a bow increases lean, allowing the player to shoot down from the horse.
Subtle head bobbing up and down while riding a moving horse.
Configuration for all of the above.

What this mod does not do (currently, may change in the future, no guarantees):
Horse armor or saddle enchantments.
Taming of undead horses. Use Universal Tweaks for that.
Automatic / AFK horse movement.
Horse calling. Quark has a whistle for this.
Work on versions other than 1.12. Not planning to change this in the foreseeable future.

With mod:

Without mod:

Leaning demo (Can look a bit odd in third person while drawing a bow):

Better Horse Movement