Greetings! Well, as our nature is, we really want the rare types of horses. So first you must have the Mo' Creatures Mod Installed. And if you do, I suggest you look everywhere, especially desert-like areas, because they appear there most often.
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Since there are no unicorns or pegasuses, no.
You can't. You have to find a unicorn, and that unicorn can breed with another, but not with horses.
You either feed it apples or wheat, then you will see the name your pet screen.
There are no rabbits in vanilla Minecraft.
You cant find a giant mob in vannilla minecraft but you can sumon him using a command or a spawner.