Ah yes Ricci, great points! I kind of left that key detail of direct contact and equipment out huh? Definitely do not allow sharing of water buckets and if they fill with a hose, don't let the hose come anywhere near your horse or her buckets come near spigots or you'll spread it to everyone else.
And Corino is right too, you should definitely plan on lots of rest for the next several weeks. I'm also a little puzzled that the vet didn't come out to confirm and see for herself just how sick your mare is.