I'm a lvl 10 mage with 99 intelligence (298 mana) but only have the beginning lvl spells and I'm just now starting to play the game.  The problem I'm running into is the animals running around the world keep attacking my horse, so I jump off my horse to fight them and my horse runs away and the animal is hot on his heels biting away at him.  The horse and animal both run faster than my character and by the time I catch up to them my horse is already dead by the time I can kill the attacking animal.  My horse has horse armor which makes this even more annoying since I don't have the 500 bones needed for more armor.

Does anyone else have this problem?  Any advice you can offer?

I don't have this problem because I never ride horses. I either fast travel or walk to my destination, discovering locations along the way.

Yeah a horse is pretty useless, and you actually paid for horse armor?  But here is a big tip, go get the wabbajack.
What kind of animals would be attacking your horse right now?  Troll?  Lion?  Wolf?

I dont ride a horse very often but when I do I find im fast enough that animals dont bother me.

I used a horse once and gave up pretty fast, It's better just not riding one