In the cold and wind your tears can often evaporate and cause symptoms of dry eyes. The lacrimal gland then produces reflex tearing - an increase in tear production intended to wash out dust or irritants (ie: cold and wind).
A pre-existing dry eye problem is often made worse in the cold or wind - this will cause the eyes to water excessively because instead of staying on the eye the extra tears spill out onto the cheeks. Treatment is often the use of an artificial tear drop such as Systane Balance which can help to stabilize the tear film. You can find artificial tear drops at a drug store (no prescription needed).