A level containing a handful or so of original/dino style horses has been released within the trees next to the Brothers House (visible within the level shown in the video).
While this is somewhat of a random implementation horses are intended to play a role throughout future Quests.
This video is showing some of the improvements made plus other neat features:
Other notable differences:
The A key is now used for the eating + firing actions as this doesn't conflict so much with dismounting (which is now only possible when you are idle with no movement keys pressed anyway) as it would with firing a weapon on a horse.
With bush eating horses your bush count starts at an intermediate number (usually 2 out of 5) as opposed to 0, you can only reach 1 or 0 by being damaged.
Speed accelerates more smoothly compared to Default where it occurs in seemingly sudden bursts.
Horses are now actually a database of different types where we will for example be able to assign different horse images different abilities and speed ranges, for instance only dino style or mechanical horses could eat bombs while life like horses would not be able to.
Horses are not a portable NPC sold in a shop like on iPhone (LOL) but are intended to be obtained throughout various places in game, although eventually certain special horses may become unlockable or made personal to a specific player.