What are the benefits of having a horse?

I recently acquired Frost after:

Successfully persuading Louis Letrush at the end of Promises to Keep.

This is my first horse, and it got me wondering about what exactly the benefits are to keeping a horse around?

I read here that horses are indeed faster than walking, and can be ridden to avoid being overencumbered. But what other benefits are there to having a horse?

Will they help me fight enemies? If so, how do they compare to myself and/or my companion (in this case Lydia)? Can they be sold for gold? If their only use is faster travel, can the be stored anywhere to stop them from dying?

What are the benefits of having a horse?

Your linked answer has almost all of the benefits, but it is missing one that I recently discovered.

If you dismount the horse while in deep water, and re-mount, your horse can run across the water at full speed.

It's great for crossing large bodies of water. There is simply no other way to get this kind of speed.