Does being mounted on a horse make fast traveling faster?
Is there any difference between:
Fast travel with no horse.
Fast travel with a horse you are not currently on.
Fast travel with a horse you are mounted on.
By difference, I mean in-game time that is consumed by the fast travel.
No, there is absolutely no difference, whether you're on foot, on a stolen horse, on a horse you own, or near a horse you own.
Tested by fast traveling between Riften stables and Markarth stables. the trip always took 26 hours and 5 minutes.
Yes, but only in one very specific instance: you're over-encumbered. Otherwise, all forms of fast travel occur at the same speed.
http://www.uesp.net/wiki/Skyrim:Horses
http://www.uesp.net/wiki/Skyrim:Carriage#Fast_Travel