Foals would definitly be at risk, but I don't think one would attack a full grown miniature.
Please think again.
We had a major problem with cougars here in 1991. There was more than one mature, full size horse attacked. One of those attacked was actually a small draft horse--the cat landed on it & clawed it up pretty bad--the horse put up a real fight & actually died of a heart attack. One was a 2 year old Quarter Horse gelding--that one survived, but he was clawed up very badly and still has the scars today. Another breeder about 6 miles west of us lost at least 2 foals to cat that summer. We had one coming around here a lot of nights--it never attacked one of our horses, but it made basket cases of them by coming to our barnyard & watching them. I have no doubt that if the cat could have caught one of them (Morgans, we didn't have Minis then) unaware, it would have attacked. The thing about cats, they tend to develop a liking for a certain type of meat--if they get horsemeat once, they will start hunting horses, at least that is what I've been told my more than one wildlife expert. Two or 3 years ago there was a horse (mature Arabian) killed by a cougar just a few miles east of here. The horse was in a corral in the yard. Nearby was a pen full of calves. The cat bypassed the calves, an easier kill, to go for the horse.
In 1991 when I called the game wardens to ask about cougars, they denied up and down that there were any cougars in southern Manitoba. I know people that actually saw the cats in this area, but the game wardens said nope, it cannot be. Two or 3 years ago when we had timberwolves come around here & I called the game warden, he pointed out that we could very well have cat too, as there's known to be cougars around. No kidding?? I said.
: A few weeks ago a game warden was in my office to look up some property ownership. I went over & asked him if Natural Resources had released some cougars here in the early 90's. (I had started to think they must have, and that's why they had been so adamant that none existed here.) He said no, the cougars just moved in here, either from Minnesota, or Alberta. So, I asked why they had denied their existence back then. He said because they just did not believe that there were any here--regardless of all the people that called to report cougar sightings (and they did get a lot of calls in 1991!) the game wardens had not seen any cougars for themselves & therefore did not believe there were any around here.
So yes, cougars actually like horse meat, and if they will attack full size horses they will surely go for a full grown Mini. A mini foal would just be an appetizer.