As the devs have stated in the Riff-rafts game development thread, tamed horses will probrably be one of the things they will be working on in the following months, so I think it is a good idea to start a thread to discuss ideas about how tamed horses should work in the game.
Personally I like the idea of being able to breed horses like we breed other tamed animals, and the quality of the horse would affect how much stamina it has, how fast stamina gets drained when running, and the total health of the horse. This way villages can actually breed their our horses and different villages will end up with different horses, some being known for their overall resistance to damage during battles and some being known for their speed and endurance.
There could also be added horse gear to the game, like horse armor, horse shoes that decrease how fast the stamina gets drained when running, etc...
Horses should eat feed from food throughs just like other tamed animals.
This would create many interesting possibilities for fun features to get added to the game, like horseback combat using lances and bows.