Are there any special horses besides the Dark Brotherhood horse?
Solution 1:
There is one - his name is Frost, and he belongs to Maven Black-Briar.
He is the only horse with a pedigree (his father is listed as Sleipnir, so take that as you will). If you hang around Riften, you will be approached by a guy who wants you to steal Frost for him. After doing so, you can decide to keep the horse by yourself (though you need to kill / intimidate the quest giver if you want to do that).
That said, he's a totally average horse otherwise. Barring console command chicanery, he's just the same as all the other non-essential horses.
Solution 2:
No, Frost is better than others but is worse than Shadowmere.
Here's a table with comparative:
http://elderscrolls.wikia.com/wiki/Horse_%28Skyrim%29
and this one too:
http://www.uesp.net/wiki/Skyrim:Horses
Solution 3:
If you have Dawnguard DLC you can obtain a spell to summon Arvak, an undead horse. The spell will last until you dismount. You can cast the spell whenever you need a horse.
And of course Dragonborn DLC lets you ride dragons.