RDR worked the same way; you tapped a few times to get the horse up to speed, then held the button and he'd stay there. In Witcher 3 you just double tap and hold and Roach will gallop all day. In MGSV it looks like the horse will just cruise along fairly slowly unless you keep urging him, though. You can see it in this demo. Go to about 20:40ish, when BB goes from a full gallop to hanging onto the side of the horse; he slows down after about 4-5 seconds. You clearly have to keep "Hyah"ing to keep him galloping.
Interesting - could be they designed it that way to substantially differentiate it from a jeep. One thing about RDR that pissed me off
hugely was that horses were basically cars. What would be the point in having a horse if you just hold a button and it 'drives' like a car? The mobility shortcoming is made up for by the fact it's less loud and less visible than a car, and you can hide off the side. All these aspects - along with the speed drop-off - are tied together. Also this:
Is there any reason to choose the horse as a buddy over the others? If you need to travel long distances you can just use the mech or even a jeep.
I'd imagine it's a pro/con trade off like this:
Car:
- faster
- can carry extra 3-4 people, conscious or no
- louder
- more visible
- not autonomous
Horse:
- fast, but slower than car
- can carry one extra person, conscious or no
- quieter
- blends in as a wild horse
- can hide off the side
- can call it to come to you
Oh, and money! I think the horse is a buddy so it's free, but it'll cost you GMP to fly a car in, each time you want one (unless you just steal one, which is risky).