I'm not a vet ..... but I am an eye doctor (human one
As danastark already mentioned, my first guess would be they are associated with the sun exposure and white skin. It could be cancerous lesions, or it could be an allergic reaction of some kind (which makes sense with watering from the eye), or some other kind of lumps/bumps that are common. I can't make a more educated guess than that without seeing what the bumps look like.
Horses (and any other kind of animal) with white skin around the eyes are indeed more prone to cancer and problems because the light pigment really reflects the light and doesn't protect well from the suns rays, unlike horses who have dark coloration around their eye. Watering eyes are certainly not uncommon because of the intense brightness can illicit a watering response (light induces the same things in humans -- makes your eyes water -- cranial nerve response).
Best thing would be to recommend to your friend to have the mysterious bumps checked out by a vet. If they would happen to turn out to be cancerous, the sooner you treat it, the better the outcome.