Anytime my does are close to birth or nursing and they lack an appetitie and seem stiff in moving, they get a calcium drench. It can't hurt and has done the job everytime I've tried it.
Does your horse have a temerature and other symptoms like your goats? The reason I ask is that I heard a story once about a lady who was having general health problems with different types of animals and it turned out there was something in her water. They did not figure it out until some family members started having problems too.