I can't tell you about horses and goats.
But about the LGD dogs, there is great hope.
My three geldings HATE dogs and learned to chase and try to harm any that entered their pasture at our former stable.
On our farm now, real ranch and goat country, we have had a total of three wandering Pyranese and Pyranese mixes wander in and spend time at our farm and with our horses.
There's something about their gentle laid-back approach that disarmed the horses in their presence. They moved slowly and didn't bark at the horses. The horses tolerated them. If one of the dogs got in their path, the horses simply laid back their ears, lowered their heads and the dogs had the sense and ability to read the horses to simply move out of their path.
I wanted badly to keep the first one that wandered onto our property for that reason but found out the little Wanderlust already had an owner.
That is the one bad thing about LGD's. Pyrs and a few of the other breeds like to wander.
Connie