Are you sure she's barking at your horses and not some other creature that passes thru at that time? I have my horses at home and I know that the deer have a routine/time they go by their pen every day.... She may be alerting you to something else...?
That was my thought as well. Is there any way for you to set up some surveillance one night (either by watching out a window, or with inexpensive game cameras, something like that) to be sure she's just barking for fun? Since she sounds like an outdoor dog I'm guessing you want her to guard, so in your shoes I'd be sure I knew she wasn't barking at something in particular before I figured out how I wanted to handle it.
FWIW, when I first got my GSD I didn't let him in my home (he was a stray and I wasn't going to keep him, and didn't want him to upset the dynamics in the house...I write a year later as I'm literally resting my laptop on him because he's passed out in my lap
), and he would bark almost every morning between 2-3 AM. I finally discovered why when I stayed up a couple of nights--we had a family of coyotes denning nearby, and they'd come around the property around that time most nights, either sniffing around my goats and chickens or just passing by on their way home from a night of hunting. I decided I didn't care to deter that behavior, even though it woke me up! I also had no indication that the coyotes were around before I got him--my coop and goat pens were very secure and I'd never noticed any sign they'd left amidst all the other dog prints and such. I would have said he was barking at nothing if you'd asked me earlier.
I don't have any specific advice about how to train this out as I don't generally keep outside dogs, but I do have major reservations about an E-collar for this circumstance for two reasons. First is, as others have said, the remote may not work through walls. Even if you test it, if the dog moves around the yard, you might have inconsistent results. Even collars designed for long ranges might be affected by the building materials and electronics in your home.
The other concern I have is that you're presumably asleep when the dog begins barking, which will make it difficult to time your correction appropriately. If you're in a particularly deep sleep and she barks 15 times before you manage to wake up fully and hit the button, then the next night you just got up for a glass of water and so you correct her on the first or second bark, I don't think it's really fair to the dog.