Will horses really run back into a burning barn?

Yes. Unfortunately, horses absolutely will try and get back into a stable that's on fire.

Horses become somewhat attached to their stalls - some horses will complain vociferously when moved and I've had a horse get away from me and run across the barn to their old stall and then threaten the animal now occupying it. When they panic, they often run "home" to their stall. (Horses at shows will sometimes run to their trailer, even ones that don't like being hauled, which may mean they're smart enough to know it's how they're going to get home).

This means that in a fire or a flood horses will often try to run back towards the danger. When evacuating horses from a fire, we make sure they are not let loose in an area where they can get back inside.