I'm pretty disappointed with my horse. He wasn't cheap -- 1000g -- but he just doesn't seem that fast. To make things worse, he's a bit of a wolf magnet and every time I get attacked I have to tediously dismount, blast the wolf, and then remount.
Is the speed of a horse actually significantly faster than normal running speed? If so, how much faster?
Not only is the horse faster (not even considering their higher base stamina -- Horses can sprint much longer than a stamina-light Dohvakiin!), but they can be ridden while encumbered.
So if two Dovahkiin (Dovahki?) were to race across a flat plain, one on a horse and the other on foot, the horse-bound hero would win every time. Horses are marginally faster
So what about when you're not traveling in a straight line?
Turns out, the horse will still win, as, despite their cumbersome turning, horses flaunt a blatant disregard for physics that can quickly turn into an incredible timesaving path.
Consider: When you're on foot, you must run around any mountains in your path.
Horses, on the other hand, have no qualms with running straight up the mountainous slopes.
Image credit to Emperorr of Reddit.
It might be that you know that you can sprint on your character, but not on your horse. Please note that your horse is also able to sprint using stamina. You can do this using the default Alt key.
Since Oblivion, they took Acrobatics and Athletics skills away, thus you can't improve your speed in such way anymore that it would be faster than a horse. The speed improvements by not being Fatigued and not being overweight are not enough to be significant.
All horses in Skyrim have the same speed and hardiness, they are all draft types that resemble a Clydesdale, and all cost 1000 septims.
All horses in Skyrim are the same, seems that they wanted to simplify the whole transportation idea.
Without mods, a horse can't be used inside a city. If you do a lot of role-playing within cities having a horse might not be useful. At the same time, characters are limited in Skyrim as Raven Dreamer noted; while you can get over some mountains by jumping left and right trying to get over a rock, a horse will be more superior in performing this task as it is less restricted by physics. You can however be smart enough to choose your path right, rather than trying to work against the physics...
In a loading text they stated that it is not faster but the horse can run for a longer time, thus making it better.
As a bonus you can still move fast on the horse, even when you are overloaded by your loot!
Alternative option, if horse is too slow, would be to become werewolf.
Werewolfs are significantly faster then horse. I preformed test to prove or bust this (unfortunatetly, I don't know how to capture screenshot in Skyrim). I started at Helgen and followed the road to Ivarstead. On horse, after 2 and half minute (duration of werewolf form) I passed the mountain and get to the "spring area" just when stopwatch hit 2:30. While in werewolf form, I hit that area around 2:10 (few seconds more or less). I believe I had time to come to Ivarstead, however, I didn't because humans are hostile while you are in wolf form. Instead, I went east towards Riften. All in all, I would say I travelled about 20% more in werewolf form. Also one thing which I noted - werewolf has way way more stamina then horse and he is freak of nature when comes to regenerating it.
Also, about your wolf problem - while in werewolf form they are friendly to you. However, note that your "wolf problem" is suddenly called "human problem". While in wolf form, you are attacked by other people in Skyrim (on horse 1 encounter with wolfs, in wolf form 2 encounters with humans - however, werewolf easly (and by this I mean realy easy) can outrun them).
The Elder Scroll Wiki says that werewolf form adds 100 stamina to you. I'm not sure about horses, but this means that wolf form sprinting time scales with your stamina (which is great if you're warrior or rogue). Just to note, I have 140 stamina while in human form.
The greatest disadvatage while you are in wolf form (if we are talking about travelling) is the fact you can't open your map, so it also depends can you remember the route by heart. I personally use this form to fast travel on the road to undiscovered areas / towns. Little tip - just rest for 24 hours if beast form fades and you still have long route ahead.
And in the end, like every true power user would say - it's 100% open source (== 0 money spent on wolf form if used for personal needs only).
P.S. Please do note that werewolf form has it's advantages and disadvantages and that you can only be in beast form for 2.5 min without feeding (not an option if you are travelling). Also, if you become werewolf, you can not become vampire (yeah, it sucks you can't be -"half vampite, half lycan, stronger then both*) To see if it suited for your playstyle follow the upper link.
*link
Right, enough about werewolfs.
There is one horse in Skyrim which "is more then just a horse". It's Shadowmere. However, unlike in Oblivion, here she is NOT faster then other horses, don't be fooled by lore. The advantage of having Shadowmere is she can fight along your side and it's considered immortal (wolf problem - gone). Oh, yeah, according to wiki, she can go where none has gone before (she can climb where you couldn't normally).
