Common thoughts about teleportation are that you can only teleport what you can carry. And unless you're a freak, you probably can't carry a horse (or horse-like animal).
An Eladrin on a horse would wind up not on a horse -- unless you invent a magic item like a special saddle which allows it to go with you.
If they make that saddle, then my eladrin WILL be putting it on our dwarf warrior.
Edition wars kill players,Dungeons and Dragons needs every player it can get.
You could also create a special mount for Eladrin that allows this. Or a feat that allows an Eladrin to convey the ability to his mount instead of himself. I'd suggest the mount be gained through extensive role playing and not gained until Paragon or Epic levels, likewise the feat should fall into one of those categories.
Some special fairy horse could be neat, yeah.
Unicorns already have the Fey Step ability as a racial power. Though it doesn't specify if a mount would be taken along. I imagine it would.
Do you mean that if an eladrin had a unicorn mount, they could teleport together? Or something else?
Well there ya go, it's already built in.
And if you don't like the whole unicorn bit just cut off the horn and call it a fey horse.
Go ahead and do that, but I think you would then have a dead fey horse ;)