On Horses and SpongeBob Squarepants (SPOILERS)

[yrthwyndandfyre]

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I have expounded in the past of the benefits of having Shadowmere, inasmuch as he costs nothing but experience, fights with you, cannot be killed, and having red eyes, is hard to miss in a herd, which helps to keep you from getting a record as a horse-thief.
I've found, though, that if I am anywhere in this world, and I fast-travel to anywhere else in this world, Shadowmere will come to me from whereever I left him.
I'm curious. For those of you who actually bought horses, how many of these characteristics do they share? Is Shadowmere unique, or do all horses do these things? I killed the Unicorn, so that option has been closed for me.
Oh, and SpongeBob Squarepants has nothing to do with this apart from the fact that it's on the TV right now, so I have that stupid jingle running through my brain.

[Daeanor]

Regular horses catch up with you whenever you fast travel. But they can be killed, and it's a crime if you kill it yourself.