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I reckon the movement is likely just as a result of keeping mechanics as close to the original (which obviously was a long time ago!), whether due to efficiency or creative reasons. The horse movement is definitely something I'd say is a design decision (in a similar manner to BotW) where the horse is not just an extension of the player character and the player coaxes it along as opposed to telling it where to go. This can indeed get a bit irritating during action sequences (as in BotW) but I quite like it as a design decision. Pardon the pun, but horses for courses!
I never played the original and as this is a remake I'm kind of judging it by current standards, which may be harsh. With the mechanics I mean the overall mechanics, there's a real lack of fluidity with each move (be it run, jump, grab etc) feeling very separate from each other. This feeling is also in the controls which are pretty clunky. The worst bit is the horse control which is just abysmal. I'm kind of getting into it anyhow as it looks great and the story line is interesting. I'm probably not doing myself any favours by playing it on hard with a baby on my shoulder, which maybe influencing my perception.