She reacted to a potential dangerous situation the horse came lose and could of caused harm to traffic /people she was disciplining it. I do think it was possibly over the top, but can you all honestly tell me you have never told a dog off for misbehaving?
She had hold of the leadrope after the horse had been caught, she then set about it a) making it more likely to become loose again as it tries to avoid being hit! And b) in the eyes of the horse she was 'disciplining' the horse for being caught and standing at the end of the leadrope, it's like horses 101 that you don't lay into a horse you've just caught because it makes them less likely to be caught in future!
She was punishing the horse for presumably not loading, pulling away and getting loose, through frustration and as horses live in the moment it won't have connected her little outburst with the fact it didn't load/pulled away and buggered off.
It's utterly shit horsemanship, but the kind of horsemanship I've seen plenty of over the years, these people may ride and keep horses, but they don't understand them and get compliance through fear rather than cooperation, because it's faster, although there'll always be something the horse fears more than you eventually.
I don't really care if she was part of a hunt or not, she was totally out of order and needs to answer for that, however I'm also no fan of Sabs, who I've seen deliberately spook horses, cause fear and hang off bits which cause pain and discomfort - while claiming to be animal lovers. Doesn't wash.