This would be a good issue to raise with your
primary care doctor, especially if it is persistent and if you find that the eye drops from the drug store are not working.
Sometimes, dry eyes during the winter are just due to irritation of the eyes by the cold and wind and dry air. In these cases, there is no real magic solution to the problem, although protecting your face when you go outside (for example using wrap around sunglasses to shield your eyes) is probably the most important step. Additionally, one of several types of artificial tears or rewetting drops might be of use. You should, however, avoid long and protracted use of "anti redness" drops, as these can, over time, actually lead to worsening of the problem.
Some people find that their dry eyes during the winter are actually the result of indoor allergies, such as mold, dust, mites, or
pet dander. In these cases, a medication to help counter the symptoms of the allergies might be the most effective thing.
Your primary care doctor can examine you for any evidence of allergy and, if those symptoms are present, help you decide which medications might be right for you.