On the face of it what she did was horrible, but as trisher says, we don't know the full story. I would say that she should definitely be banned from keeping horses (or possibly any animals) - that seems a proportionate response to the offence.
I'm not sure that huntspeople (is that a word?) have any business condemning animal cruelty from others.
I also really dislike trial by media, and social media in particular. It is a very worrying trend. When people do something wrong, they should be dealt with by the courts, calmly, with all the information to hand, and where appropriate a jury of their peers. Punishment should be limited to what has been decided and is on the statute.
Criminals should, IMO, be able to pay the penalty for their offence, learn the error of their ways, and get on with life, other than in very extreme circumstances. For someone to suffer death threats as well as losing their career, livelihood, and reputation is way over the top, I think. Public shaming is barbaric, and saying that is not to suggest that hitting animals isn't. We had moved on from public whipping and putting people in the socks, but in many ways we are returning to that sort of behaviour. 'Cancelling' people with whose views we don't agree, police forces using Facebook to show mugshots of criminals (not to mention the baying for blood in the comments) and attacking the families of those who have transgressed is, IMO, a retrograde step.
This is an interesting read on the subject, and things have got worse since it was written.