How to breed horses to get a Minecraft fairy, zorse, pegasus, etc?

You can't - those variants of horse are only possible with the Mo' Creatures mod.
- http://www.minecraftforum.net/...and-moles/

The only horse variants in "vanilla" Minecraft (the unmodded game) are regular horses, undead/zombie horses, skeleton horses, donkeys and mules. It's only possible to obtain undead/zombie and skeleton horses using the summon command as, without Mo' Creatures, they won't spawn naturally throughout the world.

The essences are only obtainable in Mo' Creatures - they do not exist in vanilla Minecraft. Again, you'd at least need to install the mod before those items and creatures are available to you. The installation method for mods (and a compatible modloader) will vary based on the version of the game you use/play.

Instead of all the compu games, try to find time to read Proverbs… Or Ecclesiastes 12, here:
[1] Remember now thy Creator in the days of thy youth…
[13] Let us hear the conclusion of the whole matter: Fear God, and keep his commandments: for this is the whole duty of man.
[14] For God shall bring every work into judgment, with every secret thing, whether it be good, or whether it be evil.

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