If I build a stable and purchase a horse for it and for some strange reason the horse dies, will it respawn or do I need to buy a new one? I think I know the answer already, just wanna be sure.

Yep, you know it. If the horse dies return to your steward and shell out a thousand gold for a new one.

I got a horse for my Lakeview house just 'cause I didn't like the look of an empty stable. I never rode it so it didn't follow me around. It stayed alive for a pretty long time though I did revert after a few bandit raids to alter history and preserve it. I think that one horse was there all the way until I accidentally deleted that PC.

Yea that's what I thought. Doesn't really matter. I don't ride them. Just like the look of what they add to the house.

I'm partial to all my horses. I have one at every house and several cities. I'll ride one to an HF house and change them out sometimes. I'm currently on the dapple grey, love the looks of it. The blacks from Whiterun were my first love but the one's from Riften are gorgeous as well.