On my first playthrough, I ran into heard of horses as soon as i left the Great Plateau, I barely managed to get one. I started to head towards Kakariko village, but ventured a little far into Hyrule Field. Before I knew it a Guardian Stalker started to chase me. With one blast from its laser it killed my horse and I was barely able to escape thanks to a nearby river. After that, scarred by what happened, knowing that I am responsible for that horses death, Link never rode a horse again.