Just found a video where some idiots thought it was a good idea to blindfold a horse and then jump on it. An unbroken horse.
That's ridiculous, but using blindfolds is perfectly legitimate under certain circumstances.
The most common time when a good handler blindfolds a horse (in an emergency you can use a sweater) is to get the horse out of a fire. Horses are really dumb when scared and will run back into a burning barn because they see their stall as the safe place. Occasionally, in an emergency, you might blindfold a horse that won't load to get it on the trailer.
Horses may also be blindfolded for some medical procedures. Dentists might blindfold the horse so the lights they are using to look at his teeth don't catch him in the eye. It is also traditional to "cup" the eye (put a hand behind the eye on one side so the horse can't see what's going on behind him) when giving injections. Blindfolding a horse can help diagnose certain neurological conditions by determining how much the horse is relying on its vision for balance. If you see a vet blindfold a horse that's just fallen at a race or event, they're checking for concussion.
Because of this, good horsemen blindfold train their horses so that they don't panic when their eyes are covered. This training is sometimes tested in competition - if you watch trail classes or "cowboy races" you might see an obstacle where the cowboy has to get off, blindfold his horse, then lead it through an obstacle.