Who are we worried about infecting who? Everybody poops... everybody's poop has bacteria and potentially parasites in it.
Chickens might be more problematic cos they roost, and might poop into the horse and goat feed/water?
My flock live in a pen (night) and pond area (day) that are enclosed by a fence which also contains my mini horse and 4 goats. Horse & goats get wormed on a regular schedule, birds do not. One important factor IMO is, are the animals confined in a small space, or spread out over a large foraging area? My birds are not swimming in the animals' drinking water, which IMO is also an important factor. The horse will occasionally drink from the pond but it's 1/3 acre, so it's not like drinking from the ducks' water pan.
Knock wood, no one's fallen ill or had diarrhea or anything yet.
Mostly I worried about someone getting stepped on, but they seem pretty savvy about that!
My vet said she didn't foresee any problems, before I opened up their forage areas. So I actually worry less now because I feel that the horse is actually a coyote/dog deterrent.