A retained testicle cannot produce sperm. If a cryptorchid horse produces sperm, it will be because he has one descended testicle. Sperm can only develop at temperatures that are lower than core body temperature. The retained testicle can and will produce testosterone, so the horse will act like a stallion. Retained testicles tend to develop malignant tumors and should be removed. The biggest problem in castrating these animals is the expense and risk of doing abdominal surgery to remove the retained testicle.
The tendency to retain a testicle is hereditary; therefore, it is unwise to breed these horses.
Merck Veterinary Manual
A "proud cut" horse refers to a gelding that was improperly castrated so that part of a testicle was left in the horse.