Any tips for preventing your horse from dying?

Solution 1:

If you care to join the Dark Brotherhood, eventually you will get Shadowmere (she returns!) who cannot be killed.

All the horse on dragon action you love, none of the ragdoll horse death!

Solution 2:

With the exception of great steed placement and healing spells there isn't much you can do. That animal just loves to stomp enemies...

Solution 3:

If you have a high enough Illusion skill, you can use the Calm or Fear spells or their higher-level versions to prevent your horse from getting involved in combat and possibly getting killed.

Playing on the PC

You could use the setessential console command to set your horse as unkillable.

The mod, Convenient Horses, can set player-owned horses to flee at the sight of combat, rather than getting involved and killed.

It can also set your horse as 'essential' (i.e. unkillable) or increase your horse's health, preventing or lessening the chances of your horse getting killed. It also has other useful, optional horse-related features.

The Oblivious Horses mod can set player-owned horses to not attack and be completely ignored by all hostile creatures and NPCs. It also has optional files that can set your horse to be unkillable.

There are also other horse-related mods that have similar features (Nexus Mods search).

Solution 4:

If my horse insists on rushing into battle, I use the Kyne's Peace shout and that takes care of my horses righteous rage.