I used to have a local farmer's tups in with my ponies from March to October each year - one or two of the youngsters would try and chase them at first but they all settled down. I wouldn't have lambs in with ponies but adult sheep are fab cross grazers which is why I keep thinking about getting a few to keep the grass tidy
or did til I ended up so short of grazing for what I already have
I'd not put goats in, personally, but I don't have experience of it so can't advise.
Just watch for mineral blocks in the field as some have copper and aren't suitable for sheep so they'd have to be tied high up where sheep can't reach..
Like the idea of a sheep rest/feed pen they can go to for a break from sharing