The answer is: It depends.
Are the horses used to being in the barn? Do they consider a stall a "safe place"? If so, they may be calmer there than they would be outside. But if the horses are used to fending for themselves outside, the sound of intense rain, hail or debris on the roof, and no way to escape it, might incite them to riot. If the horses panic inside their stalls, what will happen? Can they rear up and knock themselves out from hitting the ceiling or light fixtures? Will they kick concrete walls and break a leg? Will they try to jump out of the stall and end up straddling the wall or jam a leg through bars that are too far apart for safety? Can they break through the stall doors, and if so, what awaits them in the aisle of the barn? Can they see their fellow horses or are they isolated in their fear?Or, HORRORS! are they alone, with no comfort from other horses? If the answers are negative, the horses COULD be better off outside.
What is the condition of the structure? Is it strong enough to withstand high winds? Are there tie-downs at the corners? Shear-strength in the walls? Nothing will protect your barn from a direct hit from a tornado, but if it's passing close by and there is debris flying through the air, will the barn withstand a glancing blow?
On the other hand, if you turn your horses loose what do they face? Everyone has heard of horses (and golfers!) who shelter under trees in a thunderstorm and are killed by lightning. Do the horses have other shelter in the pasture or will they head for the trees? Is there a low spot on the property that might protect them from both lightning and the chaos of a tornado without danger of flash flooding? Horses are smart about saving themselves. They haven't survived as a species this long without knowing how. But they need options. Is the choice between a stall and a small, flat, featureless pasture where they are exposed to the elements?
What is the prevailing direction of the storms? Tornadoes typically travel from southwest to northeast. In my part of the world, rainstorms come from the south and icy spring winds come from the north, so my barn's doors open east and west. I'm surrounded on all sides by trees that cut the force of the wind as well, both at the barn and in the pasture. My horses have full access to stalls and pasture and in inclement weather PREFER to stand outside.
Given a choice, horses will often shelter up against the lee side of a building. They won't care if they get wet if they're sheltered from the wind. This is especially true if they can "bunch up" outside, but inside the stalls they are isolated and cannot find comfort from the presence of a stablemate.
How safe is it outside? In looking around your pasture and barnyard, is there "stuff" that could become missiles in strong wind? Buckets left lying around? Garbage cans? A burn pile of branches? Could a violent wind push your horse trailer through the fence? Then the broken boards or posts could become free-flying projectiles. And, speaking of that, how sturdy ARE your fences? If you turn out your horses could they escape with a little determination or panic?
You need to consider these types of questions before you can determine the answer. And, of course, the answer may be different depending on thenature of the emergency facing you. What would be considered an appropriate action for a rainstorm may not be safe in a tornado. As I mentioned, my horses aren't stabled so make their own decision about where they would be safest. Even in a raging rainstorm, which we get in the winter, I don't interfere with that decision. But, because I live in a forest, on a hilltop, in a dry climate, I have to consider wildland fires (I'm also almost on top of the San Andreas faultline!). If I were forced to evacuate immediately and for some reason couldn't take my horses, I would turn them loose and close the barn doors. I would open up all gates except the one to the road and trust them to find a route to safety. They would then have the option of hunkering down in the pond which is in a depression, or going off the back of the property and either along the ridge or down the mountain. But not everyone has the luxury of making that choice. YOUR choice may be to evacuate in the face of exteme weather to escape a dangerous home situation.
And, you might as well throw barn fires into the equation. The Connecticut Horse Council has a Horse 911 program that helps you figure out the dynamics of barn fire safety. Barns are fires waiting to happen! My book also has a chapter on barn fire safety written by the Horse 911 author, Halide Caine, and Jeff Galloway, who teaches barn fire safety classes through Emergency Training Systems. Laurie Loveman's website is dedicated to barn fire safety and has stats on barn fires that will curl your hair.
A little planning and knowledge of your own personal situation will go a long way toward protecting your horses.