I knew a little girl who broke her leg whilst falling down the second to bottom carpeted step of her staircase at home. Should her parents be sued for negligence?
My own dd knocked out two teeth by tripping over her own feet and falling against the safety gate we had put in place to protect her little brother. Does that mean I am no longer a fit parent?
As a parent, with two rather clumsy children (though thankfully now nearly grownup), I am a bit worried by the implication that every accident is the result of negligence. If we introduce this attitude towards every aspect of society, this will also be the way society judges us: that no accidents should ever happen and that if they do, it is the fault of the adult in charge who should promptly be held to account.
I feel that it will make both parents and schools paranoid of any activity that could cause physical damage. That is, any activity other than sitting still with an iPad. And we already know that an increasingly sedentary lifestyle is damaging our children.
It may well be that if the OP brings a case against the school, she will lose. But the result will also be that the school will stop outings of this type. They will feel uncomfortable and afraid next time.
And of course it is not the case that a successful court case does not cost the school: it will cost them masses in staff time, covering for whoever has to prepare the case and give witness and reassuring other parents. Those costs will not be covered by the OP.
rickety-ticket's plan seems much better: have a quiet look at the farm, discuss it quietly with the school and only act if you are sure there is a health and safety aspect that could be improved
And best wishes for a speedy recovery.