"Weepy" eyes are fairly common in many species. Excess tears, also referred to as 'epiphora', are caused by two mechanisms. The first is that the tear production, although normal in volume, is not draining through the nasolacrimal duct in the normal fashion. If your horse is young, it is possbile this duct was not formed properly and usually a simple surgery will solve the problem. The most common reason for failure of tears to drain is that the nasolacrimal duct is blocked. This may be caused by trauma, swelling, or (most commonly) dust and debris. This is routinely seen in dry dusty environments and it is a simple job for your veterinarian to flush the ducts free.
The second cause of epiphora is more serious and concerns corneal disease or inury and definitely should be checked out. The eye produces excess tears in response to inflammation or pain. Causes range from ulcers and foreign bodies to ingrown lashes or lid defects including scars and cancerous lesions. Usually epiphora from these causes are accompanied by a squinty eye as well. Danielle Bercier, DVM, Summerdale, Alabama