If you're under the gun to where you think the weather folks are going to say take cover immediately:
Keep a can of spray paint in a color that is highly visible on each horse.
Spray paint your cell phone number with area code across both sides of each horse.
I have also heard there are name tags available that can be braided into the horse's mane or forelock.
I am dead against halters (with info taped to them) because a horse can get hung up on anything while fleeing for its safety. The braided-in tags sound the most reasonable.
As far as horse in or horses out? Depends. My horses come in at night, out in the daytime, 365 days/yr. I don't change that routine for storms.
However, if they are still in the barn when a watch or warning comes across the TV, I keep them in.
Last year, a tornado literally went over top the barn and I was down there with the horses when it happened
I didn't hear anything - I mean nothing. The air was deathly still, I felt like I was in a vacuum and I could feel the hair on my neck, and see the hair on my arms being pulled straight up. All my horses stopped eating, hay hanging out of their mouths, and looked at me. I said "better start praying with me".
I had no idea there was a funnel cloud above us until later that day when the news announced a tornado had touched down in the next town and they tracked the path on TV. Between looking at that storm path and the sensation of wanting to be "sucked up", even though I was inside the barn, explained a lot
In my case, there wouldn't have been anytime to cut the horses loose. They have 22 acres with a ancient woods (big oak trees with branches big enough to be a tree) along the boundaries, there's nothing to say they would have been safe from harm out there either.
In the end it's a crap shoot, everyone has to assess their own physical environments and go with their gut