Are miniature horses safe from coyotes?

Yes and no. 

When they are in a herd of about 5 or more, and depending on how big the coyote population is. They will keep each other safe. Now that dose not mean that the coyotes will not try to go for a baby when the horses adults aren't looking. And in weening season those brand new weenlings are most at risk if they do not have an adult horse, or guard animal like a mule with them. Even then with only one guard you will still want them closer to the barn. Or close to your home where you can hear a ruckus. 

At Ferrand Triple K Farm, with our herds of 8 or more we have very little worries about coyotes but even we have the odd attack when they coyotes just have nothing to eat because of drought. We have lost only 2 babies in our 20 years of breeding. Both in times of drought, both because the babies where weened away from the adults. On the first occasion we didn't have a guard animal, hadn't learned about it yet, and we got a mule. Now my old Quarter horse Fritz is the guard for the weenlings and he loves it. On the other occasion only 3 years ago we had an extremely bad drought and their was nothing for the coyotes to eat so they took a risk. That morning we had one dead baby partially eaten and 2 dead coyotes. Now the weenlings are with Fritz in a turn out by the barn. 

Full grown Stallions that have bred, unlike mares, will chase down threats and fight them head on. Mares of all ages, the youngest being 1 year, will gather into a large group and chase predators as a giant mass of stomping running feet with the babies trailing behind them. This is a learned behavior that I have no idea what mare started it on our farm. They may have learned it from the stallions but so far other breeders are telling us its pretty unique.   

If you only have one mini and a lot of coyotes take them inside at night. One mini can do a lot of damage to one coyote but against a pack of 5 the mini doesn't stand a chance.