Back in Oblivion, when you decided that it was time to change your follower, or simply go solo, you would tell them to go home and they would. If you didn't ride your horse enough, your horse would also go home, to the stable you bought it from. The thing is that they would walk the length of Cyrodiil to get to their destination. If you told someone to wait, or just left your horse waiting for you in the wild, they would eventually get tired of waiting and head off home as well. If they weren't Essential characters there was always the chance they would get killed on the way.

Is it the same in Skyrim?

After buying Vigilance it took me all of 10 minutes to get pissed off with his constant barking, so I told him to stay at Breezehome. Fully intending to go back to get him and take him on an adventure, I've just realised that that was a couple of days ago (real-time) and, while he stayed in the house for a while, I haven't seen him since. He's also not at Riften. I've been wandering around Skyrim for a couple of months now, so I would guess there have been a couple of weeks since I left the mutt to his own devices (next to a cozy fire inside a dry house with food everywhere... the ungrateful whelp). Am I ever going to see him again? Am I likely to stumble over his corpse somewhere between Whiterun and Riften?

The same could be asked of other Followers and Horses. If I buy a horse in Whiterun, take it to Riften then buy another there and start using that one, will the Whiterun Horse wander back to Whiterun and get eaten by a pack of Wolves or trampled by Mammoths on the way? What about Followers? If I take a Follower from Riften and then dismiss her in Markarth, will she walk the breadth of Skyrim to get back home... and never make it? I think this latter is pretty important since some quests force you to dismiss your current Followers.

No idea but I plan on keeping my companions and my Loyal Horse until they die who else is going to carry my dragon scales and stollen Iron

Plus I love my horse and won't buy another unless I have no choice.

Followers can not be killed by NPC's or creatures (you can kill them with a stray AoE spell or arrow). I do not know if this applies to horses or not, but I've read many posts about people's horses dying.

I have not bought a horse yet as I am still a little bitter about the view always being 3rd person while on horseback. Plus the fact that you can't use them as pack mules it just kinda makes them useless.

I have seen videos of horses in 1st person so not sure why every says its always 3rd person.

Because it is only in third person?

Third-person only horses are not that bad. But the game was designed for first person PLUS third person. We should have an option to switch views even mounted on horses.

Im pretty sure the behaviour you describe is not in vanilla Oblivion.

Followers definitely return to their place of origin after about an ingame day or two. Possibly 3 days. Such was the case for me with Lydia. I told her to wait somewhere and I completely forgot about her after a while. I had intended to go to her last location upon arriving near it in Whiterun (I left her standing somewhere near the Jarl's place) but never retrieved her. Finally, after about 2 weeks had passed ingame, I returned to my Whiterun house to unload some items and there she sat in my chair in my bedroom.

Another case was when I took Lydia to a dungeon. Vresegge (or something like that). There was a stretch of hallways lined with traps and a powerful enemy near the end. After failing to save her hide several times, and reloading a previous save, I decided to send her home as she outlasted her usefulness forever. Once I cleared the area, I returned to my Whiterun home only to find that Lydia had not returned. I dropped my things off and went back to Vresegge (???) and wasn't able to find Lydia at all. I once again went back to Breezehome and saw Lydia in my chair in my bedroom. Though annoyed at her lack of respect for my privacy, it was good to see her back at my house.

These instances prove that followers return to their starting points after waiting for an extended period of time.

As for horses, I'm unsure. I had Shadowmere at one point, but quickly got annoyed by him following me everywhere as well as the lag he put on my system. Against my better judgement, I killed him. I don't normally use horses since there's no horse mounted battle system in place and I prefer to be ready for combat at any given time. Unmounting my horse just to fight takes away precious seconds and could be the difference between life and death. At least in my opinion.

I hope this answered your question.

You can't kill Shadowmere. ;c

Only thing Shadowmere does wrong is attack the enemy when I'm trying to sneak on by. I have learned to make sure he is very distant now ;p

If I do bring him close, it's to figure out where enemies are located and possibly tank the larger portion of it... Then I just level up my useless skills and he takes a beating but regens it within a moment's time.

Whether or not he's actually "dead" is unknown to me, but I haven't returned to the Falreath sanctuary to confirm if he resurrects or not. As far as I'm concerned at this point, he is dead. He has not returned nor has he followed me from the time I killed him. I'll check out the Falreath sanctuary to see if he respawns or not, and even if he does, I'll just send him back to the Void.

I am starting to agree that horses are more trouble than they are worth

PRO: You can fast travel over loaded...
CON: My horse thinks he/she is Achilles and any enemy within site is Hector! He/she blows my cover more times than not. This makes me 'park' him/her far away which kills the usefulness of overloaded travel.

I LOVE Shadowmere! He's always been the best horse in Oblivion and I think he's even better/tougher in Skyrim. Bandits killed 2 of my regular horses and I took to traveling with a companion all the time, so I didn't want a horse around. But now, that I have Shadowmere, I leave my companion at home and just ride into the sunset LOL!

But yes, companions should return to their point of origin... I never had a dog in Skyrim, but I think he should stay at home, if that's his place of origin. Maybe it's just a glitch?!

shadowmere can die but will resurrect in 30 days ingame where he was killed. he died at the center of the magic college when i was ambushed by an elder dragon and eventually he did respawn back

he can also die from a fall.