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:
- Any tips for preventing your horse from dying?Any tips for preventing your horse from dying?
- Is there a way to stop things from attacking my horse/NPCs and to pull them to me? Or Stop my horse/NPCs running off into combat?Is there a way to stop things from attacking my horse/NPCs and to pull them to me? Or Stop my horse/NPCs running off into combat?
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:
prid
Then, use the following command:
<prid>.ressurrect 1
Where <prid>
is the PRID of the horse. This should resurrect your horse, good as new.