I've got three horses and I've never nor ever would raise a hand to them.
I used to live in the next village to The school she teaches at and it's very horsey indeed, driving my kids to school to Oakham we would go through this village every day and always came across people on horseback or leading them in that high street.
I also used to ride at Somerby riding school too and I quickly learnt you can't say anything against hunting at all around there. ( not a fan myself even though I love horses ) again that's not a popular opinion though.
I went back to riding in my early 40's and have had horses of my own ( that I keep at home ) for the last 5 years. There's a reason I don't do livery yards ...
She probably won't lose her job and the Cottesmore hunt will wait for this to die down and go back to doing what it's always done.
My 8 yo ds's cob mare can be a little monkey when she feels like it, no one would dream of raising a hand to her she's a sentient gorgeous animal that we adore and feel lucky to share our lives with.
I'm afraid this sort of behaviour is all too common in the equestrian world, there are always videos turning up of people whacking their horse because it's 'misbehaving' I guarantee she was hitting that pony because it wasn't doing what she wanted it to. Awful, awful behaviour.