EPM protozoa is spread to horses through possum feces. So they can infect horses if they leave their feces in pastures or feed or hay. I leave them alone and just hope for the best but I can't speak for my neighbor, who has chickens.
She is kind of soft to pet. Like guard hairs on a shepherd, but softer. And her feet are warm and fleshy. More primate than rat.
The good news is that they don't eat hay, nor do they like to nest where barn cats live. The only worry about feces or urine from possums causing EPM in horses is if your hay storage area has something to eat in it, such as cat food left out. If not, they will be happy to visit your farm and significantly reduce the population of bugs (they even eat ticks), but your horses should be safe.
Thanks, guys. There is a family joke about me and possums. Years ago, I went out to the hay barn to check on the cows after dark. The single light cast a small amount of light in a little area. As I was looking for something in the barn, I heard something on the shelf next to me. I assumed it was the cat, because she always jumps up there for petting. I reached my hand over to pet her, absent-mindedly, but something wasn't quite right. The cat was black, but I saw something grey out of the corner of my eye. When I looked, my hand was hovering about an inch above a full grown possum. He was eyeing my hand, but was quite peaceful. Now, I realize it was because I was moving slowly. He didn't get petted, but almost, lol!
So, if you startle a possum, move slowly and back up to let them go on their way. They should calm down a bit. They are nocturnal, but are sometimes seen in the daytime, but usually only if disturbed by a cat, dog, or other predator. Pick up your cat bowls at night. Lock up your chickens at night. If you make your coop rat-proof, it will definitely be possum proof.