All these would be good suggestions if she owned the property she has the horse on, but unfortunately, she's taking advantage of a good situation and has almost free board right now, she just has to supply his feed. It's not a long-term problem, as eventually she's planning on moving him to either horse property that we buy together or to a proper barn. Right now he's 1.5 years old and she's just waiting for him to grow up. Once he's grown, she'll want facilities.
Anyway, there's no power within 100 yards and even so, it would mean asking the land owner to run a cord from his house, which just isn't going to happen (he wants the horse to make his trophy ranch look like a real ranch, but not too real). I was hoping there was an easy solution, but the best I've seen is a combination of several of the suggestions here and elsewhere, burying the trough partway to capture the heat of the earth, then circulating with a bubbler. Even that sounds dubious in these extreme colds. Tomorrow is supposed to get down to -1F with a high of 11F.
Ah, well, such is life. It's only one winter and right now it's a heck of a bargain.