Yup, and they can be just as annoying as when we get them. Hives on horses are caused by the same things - a skin irritant or allergy. They can be extremely visible on horses, and appear as raised welts with the hair standing up vertically.
They're most often found on the neck and shoulder. Hives is easy to diagnose, but tracing the cause can be very hard. Hives can be caused by medication, fly spray, food allergies, heat and stress. I've even known it to be caused by an allergy to the laundry detergent used to wash a rug.
The symptoms are relieved with a fast-acting corticosteroid injection or in extreme cases (such as if the horse is having difficulty breathing) with epinephrine. Fortunately, many cases of hives are mild enough to be treated with NSAIDS. Antihistamines do not work well for horses with hives.