"As a Trust we are committed to ensuring the best standard of education for all of our young people and we look forward to continuing this throughout the 2021/22 academic year and beyond", the organisation said in a statement.
"The welfare of horses and ponies is of the utmost importance to The Pony Club, therefore the lady in question has been removed from her voluntary position as a team organiser for a Branch", the organisation said in a statement.
A neighbour of Sarah Moulds told the Mail on Sunday that the woman was forced to move to another location after she received vast amounts of "vile" abuse on social media as well as death threats.
"I don't know what happened and in what context but what is now happening to Sarah is horrible. She's terrified of being in her own home in case someone targets her or her kids there. It's awful and has got very much out of hand. She fears for her life", the neighbour said.
"I've seen the video but we don't know what the horse had been doing and if it was out of control. But we know it ran out onto the road and she told it off. She was reprimanding the horse. There was no malice intended. She is very well thought of and respected", he said.