I have found it very interesting that my mares with new foals, while very protective and agressive toward other horses, don't mind my LGD, Tanna, being close to their newborns.
I introduce the Tanna to the foals when they are first born, and she can see the foals in the stalls. When the mare and foal is turned out, Tanna follows them at a distance and observes, and the mare generally allows her to get as close as she likes, though Tanna is very cautious. After that, you always know where the newest foal is, because Tanna will be shadowing it, lying nearby and keeping guard. I think that even the mares feel reassured by her presence.
You don't just put a dog, even an LGD, out with your herd and see what happens, though. You start when they are young, you keep them near their future charges to let them bond to them, but keep them protected from the horses as well, so they aren't bitten or stomped and learn to fear or dislike the horses. Then you need to closely supervise their interactions so that any misbehavior can be corrected. I got a two year old LGD just a few months ago, and though he lived with miniature horses in his previous home and did great, he still went through a probationary and getting-to-know-you time when he first got here, because he had never lived with MY horses, and I wanted to know how he acted and get him feeling at home before he was turned out with the horses.
I just found out that not only do we have coyotes that I didn't know about, and cougars that I did know about, but that there are also three wolves in the area as well, so I value my LGD's more now than ever!