I'm wondering how the hell this woman thought it was okay to grab a horse's reins without asking the rider

King's Guard shouts at woman who grabs horse's reins but people can't decide who is in the wrong

Reins (on a horse) is the equivalent of the steering wheel of a car

And also, you wouldn't grab the harness of a working assistance dog, so don't do it to a working horse. Doing so is putting everyone around there, in danger. In the same way as grabbing the steering wheel of someone's car and pulling it in one direction and expecting it t not go where you just told it to, is dangerous.