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.
I've had success with a few things when it comes to people following me. I'm not on a sneaky character, so I've had to get crafty for some missions. It sounds like you've tried some of these methods already, but I'll put them here anyway just for completion's sake.
One is to try during the day, when people are out and about or tending to their stores. I've noticed that some (not all) vendors will stay at their counters instead of following me.
Second, is to go in and scout a quick path while letting the person follow you, but not steal anything. Then, go out and come back in (this usually resets their position) and make a mad dash for whatever you needed to get. I may just be lucky at encountering slow people, even in Solitude. I'm not sure if their speed or concern with me stealing something is related to anything.
Finally, I've also had success with telling my companion to wait on the stairs or in smaller door ways to block the person from following me, or at least slow them down more. It seems to be hit and miss, but it's worth a try.
I've also read (and it's mentioned in a comment above) that buckets/pots on heads can work. I've never tried it myself, but it would be a lot funnier than any of my suggestions! Maybe some combination of buckets and companion blocking to slow them down would help.
Best Answer
There is no way to see your horse's health without attacking it yourself, sorry.
But for tips on how to keep your horse from dying, check out:
If you're willing to bend a few rules, you could also try resurrecting your horse via the console.
First, find the horse's PRID: you can do that by opening up the console, selecting the horse, and using the following command:
Then, use the following command:
Where
<prid>is the PRID of the horse. This should resurrect your horse, good as new.