I know the game you're talking about. It was definitely very sudden and shocking in that game. But I felt zero attachment to the horse. In Ghost, the horse is basically your only travel companion. And you talk to it every time you ride. Made the death more impactful for me.
For me personally, I built a relationship with the horse in that game. It was all completely organic, too. It developed over the course of the game, so when my horse was taken from me, I was legitimately shocked. The fact that I could have just grabbed another horse at any given moment, but I hadn't, made it feel even more powerful. I felt even more responsible.
In GoT there are all those little cutscenes that play after every event you clear, and I felt like they were trying to create a bond that I never felt. It just didn't work as well for me.