There are three different horse textures (white, brown, black) which will spawn on green grassy areas and dry dirt areas in Ethereal mapgen.
Horses can be tamed with 10x wheat, apple, barley, oats of corn which then allows the player to pick up the horse using a lasso and ride by right-clicking with a saddle.
Right clicking a horse with a saddle equips it and the horse will be ordered to stand still until you wish to ride.
Horseshoes can be crafted using steel, bronze, mese, diamond and crystal (4x ingots - 2 down either side with 1x block top middle) and placed on a horse by right clicking with the item. These can make horses run faster or jump higher while riding depending on tier.
When riding a horse monsters will generally attack the horse first to get to player riding it, when horse dies the player is dismounted and it will drop any shoes or saddles in use as well as some horse meat.