Here in the South, we call them possums. Same animal, less enunciation. 
They do carry EPM, but it shouldn’t be a problem if you keep your hay on pallets and don’t put the cat food on it. In fact, keeping your barn doors closed, with a high entry spot for cats, will reduce the chance of possums (or opossums) coming into your barn at night. Feeding your horses in feeders helps, too.
The thing is, as was explained to me by UF vets, we have really high rates of EPM exposure down here in Florida and it’s because possums pee and poop in pastures while they hunt down those crickets and grasshoppers that eat your grass and reduce forage available to horses. Horses down here WILL be exposed, but only some will get sick. Many of us have learned to live with them because they also reduce tick populations.
The fancy barns annihilate every living thing in the vicinity. I’m sure they don’t see possums, but at the cost of heavy pesticide exposure.
The last part is about rabies. Possums can’t get rabies and they are extremely efficient bug eaters. They are great to have roaming on farms. I rescue possums and release them into our woods. Since they can range for a mile or two at night and never sleep in the same spot more than 2-3 nights, they move on quickly. They can’t get into our horse barn at night, so we don’t have issues. They do go into our cow barn and forage through the fallen hay for bugs. They do a terrific job! They are incredible little creatures.