Horses with long manes for show purposes, like the Arab mentioned in the question, might fare well with their manes French-braided to avoid having the heat trapped against the neck. Small individual braids will break the hair, but a French braid directly down the top of the neck that is redone every few days will keep long manes intact. Other, more serious hair loss can stem from dermatophyte infections. Before purchasing and applying products for these conditions, you should make sure that is, in fact, the cause of the hair loss. This substance costs around three dollars for a jar and has a color indicator that will decipher whether the fungus is the airborne type that lands on hair all the time, or if it's a serious dermatophyte that requires more rigorous treatment.
Some veterinarians use iodine or prescription anti-fungals.
It is not recommended to use home remedies such as Clorox, as these agents will burn the skin. For proven ringworm, a problem arises when topical anti-fungal ointments sit on top of the skin and surrounding hair and do not reach the hair follicle, where it is needed. A soft toothbrush will solve this matter if used to brush the medication in at the base of the hair. Dry the area with a clean towel. Most importantly, communicate with your veterinarian about the condition and avoid home remedies.