To kill the aliens that come to steal the cows, you must shoot them with arrows, then keep chasing and shooting them because they will continue to regenerate until 6am.
A good tactic that I used is to stay near the barn, and to not go very far from it. But if you're out of arrows or one of "Them" is getting behind the barn, it helps to use the Bunny Hood, which you can get the day that you arrive at Romani Ranch. But whatever you do, DO NOT USE EPONA UNLESS YOU'RE FLAWLESS WITH HER. It's very hard to shoot "Them" and control Epona at the same time. So, good luck!
Why does everyone advise that you don't use Epona? I'm not exactly 'flawless' with her, I don't think, but I was still able to use her quite well against 'Them'. To answer the question, though, I just ride in circles around the barn and the house and shoot anything that comes near it. Also, play the Inverted Song of Time, because 'They' move slower when the flow of time is slowed.
You shoot them with arrows. I highly advise you don't use epona;stay near the house and shoot them.