Young horse grow naturally over a few days of "chunk is loaded" time.
They also grow very slightly on food bribes (early game it's just not worth it).
Young horses that you breed yourself are born untamed.
Preventing a wild horse from being eaten by a zombie at night:
If there are tunnels entrances nearby, push horse away from the entrances, or block entrances with blocks.
Free-roaming horses can flee from zombies, semi-reliably surviving zombie chases. But not always, tough.
Making a nearby "tiny outpost" where you go to bed right at 9 o'clock, that can work, but it is a risk.
Best approach is to simply leave the horse well before sunset and move far away so that the horse is far enough into unloaded chunks territory that even if a helmet-wearing zombie survived the night from your loaded chunks territory, it would not roam about to "find" a too-close-nearby horse.
Preventing a horse that is in the wilderness from moving away between taming attempts:
- Attaching horse to a Lead to a Fence will not work:
MITE is buggy that way. Whenever chunk reloads, Leads just fall to the ground. Bummer.
- Four 2-high pillars, placed as below:
. = ground
S = 2-high soft blocks (dirt, sand, or gravel)
+ = "horse enclosure"
Not 100% perfect but very quick and cheap to do.
- Covered hole:
2x2 hole in ground, 3 deep. Push horse inside. Fully cover hole with inverted slabs.
I think the various food give the horse the same "temper" (docility) bonus as in vanilla.
So, cheapest and easiest ones are Sugar or Wheat. Everything else is a waste.
- Odds of taming depend on horse's "docility":
Food bribes and taming attempts both help.
Harming the horse has a negative effect.
- First bribing + taming attempt:
Never "bribed" horses will flee even sooner (and faster!) from you.
So, prepare bribing food in your active direct inventory slot in advance,
then use "Jumping while running" to help you catch up to the horse.
- To climb on horse, right-click from an empty Direct Inventory Slot.
Horse will move randomly, sometimes less than a second, sometimes more than 30 seconds.
Then one of two things happen:
- Horse kicks you. You might also take some damage, so... don't try to tame a horse while low on life!
- Horse stops, gives hearts animation (if particles aren't Off), and is tamed and ready to accept a Saddle.
Delay before being able to bribe again: 4000 ticks = 3 minutes 20 seconds.
Delay before being able to ride again: 4000 ticks = 3 minutes 20 seconds.
Best taming approach:
When exploring, bring Saddle + food bribe, just in case you find a horse.
Bribe with food before each taming attempt.
Try taming 3/day: early morning, noon, late afternoon.
In between taming attempts, leave well before sunset.
Build horse enclosure at your main base before bringing it back home.